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Journal articles on the topic 'Regular ordered semigroup'

Author: Grafiati
Published: 3 June 2025
Last updated: 23 June 2025

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1

Pinto, G. A. "Eventually Pointed Principally Ordered Regular Semigroups." Sultan Qaboos University Journal for Science [SQUJS] 24, no. 2 (2020): 139. http://dx.doi.org/10.24200/squjs.vol24iss2pp139-146.

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An ordered regular semigroup, , is said to be principally ordered if for every there exists . A principally ordered regular semigroup is pointed if for every element, we have . Here we investigate those principally ordered regular semigroups that are eventually pointed in the sense that for all there exists a positive integer, , such that . Necessary and sufficient conditions for an eventually pointed principally ordered regular semigroup to be naturally ordered and to be completely simple are obtained. We describe the subalgebra of generated by a pair of comparable idempotents and such that .
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2

Çullhaj, Fabiana, та Anjeza Krakulli. "On an equivalence between regular ordered Γ-semigroups and regular ordered semigroups". Open Mathematics 18, № 1 (2020): 1501–9. http://dx.doi.org/10.1515/math-2020-0107.

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3

Sajjad, Tehrim, Muhammad Izhar, Asghar Khan та Kostaq Hila. "Onint-soft quasi-Γ-ideals of an ordered Γ-semigroup". Filomat 38, № 13 (2024): 4511–28. https://doi.org/10.2298/fil2413511s.

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In this paper, we introduce the concept of int-soft ?-semigroup, int-soft quasi-?-semigroup and int-soft left (resp., right) ?-semigroup of ordered ?-semigroup over an initial universal set U. We investigate some properties of int-soft quasi-?-ideals and left (resp., right) ?-ideals of ordered ?-semigroup. Moreover, we define critical soft point of ordered ?-semigroup. By using the notion of critical soft point, we define semiprime int-soft quasi-?-ideals of ordered ?-semigroups. Characterizations of completely regular ordered ?-semigroups in terms of their int-soft quasi-?-ideals and semiprime int-soft quasi-?-ideals are provided. Furthermore, we define the semilattices of left and right simple sub-?-semigroups of ordered ?-semigroups and characterize them in terms of their int-soft quasi-?-ideals.
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4

Xie, Xiang-yun. "On Strongly Ordered Congruences and Decompositions of Ordered Semigroups." Algebra Colloquium 15, no. 04 (2008): 589–98. http://dx.doi.org/10.1142/s1005386708000564.

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In this paper, we introduce the concept of a strongly ordered congruence on a directed ordered semigroup S. We prove that any strongly ordered congruence on S is a strongly regular congruence. We characterize the finite direct product, subdirect product and full subdirect product of ordered semigroups by using the concepts of strongly ordered congruence and regular congruence on an ordered semigroup S.
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5

Kumar Bhuniya, Anjan, and Kalyan Hansda. "On Radicals of Green’s Relations in Ordered Semigroups." Canadian Mathematical Bulletin 60, no. 2 (2017): 246–52. http://dx.doi.org/10.4153/cmb-2016-093-7.

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AbstractIn this paper, we give a new definition of radicals of Green’s relations in an ordered semigroup and characterize left regular (right regular), intra regular ordered semigroups by radicals of Green’s relations. We also characterize the ordered semigroups that are unions and complete semilattices of t-simple ordered semigroups.
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6

Sadhya, Shauli, and Kalyan Hansda. "Generalized Green's relations and GV-ordered semigroups." Quasigroups and Related Systems 30, no. 1(47) (2022): 161–68. http://dx.doi.org/10.56415/qrs.v30.14.

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In this paper an extensive study of the concepts of generalized Green’s relations and GV -semigroups without order to ordered semigroups have been given. Our approach allows one to see the nature of generalized Green’s relations in the class of GV -ordered semigroups. Moreover we show that an ordered semigroup S is a GV -ordered semigroup if and only if S is a complete semilattice of completely π-regular and Archimedean ordered semigroups.
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7

Habib, Sana, Harish Garg, Yufeng Nie, and Faiz Muhammad Khan. "An Innovative Approach towards Possibility Fuzzy Soft Ordered Semigroups for Ideals and Its Application." Mathematics 7, no. 12 (2019): 1183. http://dx.doi.org/10.3390/math7121183.

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The objective of this paper is put forward the novel concept of possibility fuzzy soft ideals and the possibility of fuzzy soft interior ideals. The various results in the form of the theorems with these notions are presented and further validated by suitable examples. In modern life decision-making problems, there is a wide applicability of the possibility fuzzy soft ordered semigroup which has also been constructed in the paper to solve the decision-making process. Elementary and fundamental concepts including regular, intra-regular and simple ordered semigroups in terms of possibility fuzzy soft ordered semigroup are presented. Later, the concept of left (resp. right) regular and left (resp. right) simple in terms of possibility fuzzy soft ordered semigroups are delivered. Finally, the notion of possibility fuzzy soft semiprime ideals in an ordered semigroup is defined and illustrated by theorems and example.
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8

Abbasi, Mohammad Yahya, Abul Basar та Akbar Ali. "A characterization of ordered Γ-semigroups by ordered (m,n)-Γ-ideals". Boletim da Sociedade Paranaense de Matemática 39, № 4 (2021): 165–74. http://dx.doi.org/10.5269/bspm.41186.

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In this paper, we study (m,n)-regular ordered Γ-semigroups through ordered (m,n)-Γ-ideals. It is shown that if (S,Γ,·,≤) is an ordered Γ-semigroup; m,n are non-negative integers and A(m,n) is the set of all ordered (m,n)-Γ-ideals of S. Then, S is (m,n)-regular⇐⇒ ∀A ∈ A(m,n), A = (AmΓSΓAn]. It is also proved that if (S,Γ,·,≤) is an ordered Γ-semigroup and m,n are nonnegative integers and R(m,0) and L(0,n) is the set of all (m,0)-Γideals and (0,n)-Γ-ideals of S, respectively. Then, S is (m,n)-regular ordered Γ semigroup ⇐⇒∀R ∈R(m,0)∀L ∈L(0,n),R∩L = (RmΓL∩RΓLn].
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9

Shoji, Kunitaka. "Regular Semigroups Which Are Amalgamation Bases for Finite Semigroups." Algebra Colloquium 14, no. 02 (2007): 245–54. http://dx.doi.org/10.1142/s1005386707000247.

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In this paper, we prove that a completely 0-simple (or completely simple) semigroup is an amalgamation base for finite semigroups if and only if it is an amalgamation base for semigroups. By adopting the same method as used in a previous paper, we prove that a finite regular semigroup is an amalgamation base for finite semigroups if its [Formula: see text]-classes are linearly ordered and all of its principal factor semigroups are amalgamation bases for finite semigroups. Finally, we give an example of a finite semigroup U which is an amalgamation base for semigroups, but not all of its principal factor semigroups are amalgamation bases either for semigroups or for finite semigroups.
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10

Gambo, Ibrahim, Nor Haniza Sarmin, Hidayat Ullah Khan, and Muhammad Faiz Khan. "The characterization of regular ordered Gamma semigroups in terms of (E,EVq_k)-fuzzy Gamma ideals." Malaysian Journal of Fundamental and Applied Sciences 13, no. 4 (2017): 576–80. http://dx.doi.org/10.11113/mjfas.v0n0.608.

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The advancement in the fascinating area of fuzzy set theory has become area of much interest, generalization of the existing fuzzy subsystems of other algebraic structures is very important to tackle more current real life problems. In this paper, we give more generalized form of regular ordered gamma semigroups in terms of (E,EVq_k)-fuzzy gamma ideals. Particularly, we characterized left regular, right regular, simple and completely regular ordered gamma semigroups in terms of this new notion. Some necessary and sufficient conditions for ordered gamma semigroup to be completely regular are provided in this paper.
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11

MALLICK, SUSMITA, and KALYAN HANSDA. "On the Semigroup of Bi-Ideals of an Ordered Semigroup." Kragujevac Journal of Mathematics 47, no. 3 (2023): 339–45. http://dx.doi.org/10.46793/kgjmat2303.339m.

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The purpose of this paper is to characterize an ordered semigroup S in terms of the properties of the associated semigroup B(S) of all bi-ideals of S. We show that an ordered semigroup S is a Clifford ordered semigroup if and only if B(S) is a semilattice. The semigroup B(S) is a normal band if and only if the ordered semigroup S is both regular and intra regular. For each subvariety V of bands, we characterize the ordered semigroup S such that B(S) ∈ V.
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12

Cheng, Qi, Feng Lian Yuan, Yun Qiang Yin та Qing Yan Chen. "Regular (ϵ,ϵνqk) - Fuzzy Duo Ordered Semigroups". Advanced Materials Research 756-759 (вересень 2013): 3084–88. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.3084.

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In this paper, the ideal of quasi-coincidence of a fuzzy point with a fuzzy set is generalized and the concept of an - fuzzy ideal (bi-ideal, quasi-ideal) of an ordered semigroup is introduced. The the notion of - fuzzy duo ordered semigroups is introduced and some characterization theorems are presented in terms of - fuzzy ideals.
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13

Blyth, T. S., and G. A. Pinto. "Residuated regular semigroups." Proceedings of the Edinburgh Mathematical Society 35, no. 3 (1992): 501–9. http://dx.doi.org/10.1017/s0013091500005770.

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We prove that in a residuated regular semigroup the elements of the form and are idempotents, and derive some consequences of this fact. In particular, we show how the maximality of such idempotents is related to the semigroup being naturally ordered, and obtain from this a characterisation of the boot-lace semigroup of [2].
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14

Khan, Faiz Muhammad, Nie Yufeng, Hidayat Ullah Khan та Bakht Muhammad Khan. "Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals". Advances in Fuzzy Systems 2018 (10 червня 2018): 1–10. http://dx.doi.org/10.1155/2018/5304514.

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A new trend of using fuzzy algebraic structures in various applied sciences is becoming a central focus due to the accuracy and nondecoding nature. The aim of the present paper is to develop a new type of fuzzy subsystem of an ordered semigroup S. This new type of fuzzy subsystem will overcome the difficulties faced in fuzzy ideal theory of an ordered semigroup up to some extent. More precisely, we introduce ∈,∈∨qkδ-fuzzy left (resp., right, quasi-) ideals of S. These concepts are elaborated through appropriate examples. Further, we are bridging ordinary ideals and ∈,∈∨qkδ-fuzzy ideals of an ordered semigroup S through level subset and characteristic function. Finally, we characterize regular ordered semigroups in terms of ∈,∈∨qkδ-fuzzy left (resp., right, quasi-) ideals.
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15

Bashir, Shahida, Medhit Fatima, and Muhammad Shabir. "Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals." Mathematics 7, no. 3 (2019): 233. http://dx.doi.org/10.3390/math7030233.

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Our main objective is to introduce the innovative concept of (α,ß)-bipolar fuzzy ideals and (α,ß)-bipolar fuzzy generalized bi-ideals in ordered ternary semigroups by using the idea of belongingness and quasi-coincidence of an ordered bipolar fuzzy point with a bipolar fuzzy set. In this research, we have proved that if a bipolar fuzzy set h = (S; hn, hp) in an ordered ternary semigroup S is the (∈,∈ ∨ q)-bipolar fuzzy generalized bi-ideal of S, it satisfies two particular conditions but the reverse does not hold in general. We have studied the regular ordered ternary semigroups by using the (∈,∈ ∨ q)-bipolar fuzzy left (resp. right, lateral and two-sided) ideals and the (∈,∈ ∨ q)-bipolar fuzzy generalized bi-ideals.
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16

Romano, Abraham. "On regular anti-congruence in anti-ordered semigroups." Publications de l'Institut Math?matique (Belgrade), no. 95 (2007): 95–102. http://dx.doi.org/10.2298/pim0795095r.

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For an anti-congruence q we say that it is regular anti-congruence on semigroup (S,=, _=, ?, ?) ordered under anti-order ? if there exists an antiorder ? on S/q such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anti-congruence q is regular if there exists a quasi-antiorder ? on S under ? such that q = ? ? ??1. Besides, for regular anti-congruence q on S, a construction of the maximal quasi-antiorder relation under ? with respect to q is shown.
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17

Sanpan, Hataikhan, Pakorn Palakawong na Ayutthaya, and Somsak Lekkoksung. "On (m, n)-Fuzzy Sets and Their Application in Ordered Semigroups." International Journal of Analysis and Applications 23 (April 14, 2025): 90. https://doi.org/10.28924/2291-8639-23-2025-90.

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In this paper, we introduce the concepts of (m, n)-fuzzy subsemigroups, (m, n)-fuzzy left (right, two-sided, bi-, (1, 2)-) ideals of an ordered semigroup and some their algebraic properties are studied, thereafter the relationship among their (m, n)-fuzzy ideals was investigated. Moreover, we characterize left (resp., right, two-sided, bi-) ideals by using (m, n)-fuzzy left (resp., right, two-sided, bi-) ideals. Finally, we characterize regular ordered semigroups and intra-regular ordered semigroups in terms of (m, n)-fuzzy left ideals, (m, n)-fuzzy right ideals, and (m, n)-fuzzy bi-ideals.
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18

Linesawat, Krittika, and Somsak Lekkoksung. "A Study on Multi-Intuitionistic Fuzzy Sets and Their Application in Ordered Semigroups." International Journal of Analysis and Applications 23 (March 7, 2025): 63. https://doi.org/10.28924/2291-8639-23-2025-63.

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In this paper, we introduce the notion of multi-intuitionistic fuzzy sets in ordered semigroups. The concepts of multi-intuitionistic fuzzy subsemigroups, multi-intuitionistic fuzzy left (right, two-sided, interior) ideals of an ordered semigroup are introduced and some algebraic properties of multi-intuitionistic fuzzy subsemigroups and such their multi-intuitionistic fuzzy ideals are studied. Moreover, the relationships among their multi-intuitionistic fuzzy ideals are investigated. We prove that in regular, intra-regular, and semisimple ordered semigroups, the concepts of multi-intuitionistic fuzzy interior ideals and multi-intuitionistic fuzzy ideals coincide. Finally, the new multi-intuitionistic fuzzy sets are considered.
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19

Hila, Kostaq, та Edmond Pisha. "On Lattice-Ordered Rees Matrix Γ-Semigroups". Annals of the Alexandru Ioan Cuza University - Mathematics 59, № 1 (2013): 209–18. http://dx.doi.org/10.2478/v10157-012-0033-8.

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Abstract The purpose of this paper is to introduce and give some properties of l-Rees matrix Γ-semigroups. Generalizing the results given by Guowei and Ping, concerning the congruences and lattice of congruences on regular Rees matrix Γ-semigroups, the structure theorem of l-congruences lattice of l - Γ-semigroup M = μº(G : I; L; Γe) is given, from which it follows that this l-congruences lattice is distributive.
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20

Blyth, T. S., and G. A. Pinto. "Principally ordered regular semigroups." Glasgow Mathematical Journal 32, no. 3 (1990): 349–64. http://dx.doi.org/10.1017/s0017089500009435.

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An ordered semigroup S will be called principally ordered if, for every x ɛ S, there existsx* = max {y ɛ S; xyx ≤ x}.Here we shall be concerned with the case where S is regular. We begin by listing some basic properties that arise from the above definition. As usual, we shall denote by V(x) the set of inverses of x ɛ S.
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21

Khan, Hidayat Ullah, Nor Haniza Sarmin, Asghar Khan, and Faiz Muhammad Khan. "Classification of Ordered Semigroups in Terms of Generalized Interval-Valued Fuzzy Interior Ideals." Journal of Intelligent Systems 25, no. 2 (2016): 297–318. http://dx.doi.org/10.1515/jisys-2015-0035.

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AbstractSeveral applied fields dealing with decision-making process may not be successfully modeled by ordinary fuzzy sets. In such a situation, the interval-valued fuzzy set theory is more applicable than the fuzzy set theory. Using a new approach of “quasi-coincident with relation”, which is a central focused idea for several researchers, we introduced the more general form of the notion of (α,β)-fuzzy interior ideal. This new concept is called interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal of ordered semigroup. As an attempt to investigate the relationships between ordered semigroups and fuzzy ordered semigroups, it is proved that in regular ordered semigroups, the interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy ideals and interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals coincide. It is also shown that the intersection of non-empty class of interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals of an ordered semigroup is also an interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal.
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22

Mahboob, Ahsan, Abdus Salam, Md Firoj Ali, and Noor Mohammad Khan. "Characterizations of Regular Ordered Semigroups by (∈,∈∨(k∗,qk))-Fuzzy Quasi-Ideals." Mathematics 7, no. 5 (2019): 401. http://dx.doi.org/10.3390/math7050401.

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In this paper, some properties of the ( k ∗ , k ) -lower part of ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideals are obtained. Then, we characterize regular ordered semigroups in terms of its ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideals, ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy generalized bi-ideals, ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy left ideals and ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy right ideals, and an equivalent condition for ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy left (resp. right) ideals is obtained. Finally, the existence theorems for an ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideal as well as for the minimality of an ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideal of an ordered semigroup are provided.
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23

Blyth, T. S., and M. H. Almeida Santos. "On weakly multiplicative inverse transversals." Proceedings of the Edinburgh Mathematical Society 37, no. 1 (1994): 91–99. http://dx.doi.org/10.1017/s001309150001871x.

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We show that an inverse transversal of a regular semigroup is multiplicative if and only if it is both weakly multiplicative and a quasi-ideal. Examples of quasi-ideal inverse transversals that are not multiplicative are known. Here we give an example of a weakly multiplicative inverse transversal that is not multiplicative. An interesting feature of this example is that it also serves to show that, in an ordered regular semigroup in which every element x has a biggest inverse x0, the mapping x↦x00 is not in general a closure; nor is x↦x** in a principally ordered regular semigroup.
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24

Kaewchay, Saowapak, Ronnason Chinram, and Montakarn Petapirak. "Ordered semigroups containing covered (m,n)-ideals." Gulf Journal of Mathematics 19, no. 1 (2025): 169–77. https://doi.org/10.56947/gjom.v19i1.2537.

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In this article, we extend the concept of covered (m, n)-ideals by defining covered (m, n)-ideals of ordered semigroups, where m, n are nonnegative integers. The results obtained generalize those of covered one-sided ideals and covered bi-ideals. We additionally investigate the conditions under which, in an (m, n)-regular ordered semigroup S, every covered (m, n)-ideal of an (m, n)-ideal I of S is also a covered (m, n)-ideal of S.
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25

Kehayopulu, Niovi. "On ordered hypersemigroups with idempotent ideals, prime and weakly prime ideals." European Journal of Pure and Applied Mathematics 11, no. 1 (2018): 10. http://dx.doi.org/10.29020/nybg.ejpam.v11i1.3085.

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Some well known results on ordered semigroups are examined in case of ordered hypersemigroups. Following the paper in Semigroup Forum 44 (1992), 341--346, we prove the following: The ideals of an ordered hypergroupoid$H$ are idempotent if and only if for any two ideals $A$ and $B$ of $H$, we have $A\cap B=(A*B]$. Let now $H$ be an ordered hypersemigroup. Then, the ideals of $H$ are idempotent if and only if $H$ is semisimple. The ideals of $H$ are weakly prime if and only if they are idempotent and they form a chain. The ideals of $H$ are prime if and only if they form a chain and $H$ is intra-regular. The paper serves as an example to show how we pass from ordered semigroups to ordered hypersemigroups.
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26

Jun, Young Bae, Seok Zun Song, and G. Muhiuddin. "Concave Soft Sets, Critical Soft Points, and Union-Soft Ideals of Ordered Semigroups." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/467968.

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The notions of union-soft semigroups, union-softl-ideals, and union-softr-ideals are introduced, and related properties are investigated. Characterizations of a union-soft semigroup, a union-softl-ideal, and a union-softr-ideal are provided. The concepts of union-soft products and union-soft semiprime soft sets are introduced, and their properties related to union-softl-ideals and union-softr-ideals are investigated. Using the notions of union-softl-ideals and union-softr-ideals, conditions for an ordered semigroup to be regular are considered. The concepts of concave soft sets and critical soft points are introduced, and their properties are discussed.
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27

Khalaf, Mohammed M., Faisal Yousafzai, and Muhammed Danish Zia. "On smallest (generalized) ideals and semilattices of (2,2)-regular non-associative ordered semigroups." Boletim da Sociedade Paranaense de Matemática 40 (January 1, 2022): 1–13. http://dx.doi.org/10.5269/bspm.42419.

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An ordered AG-groupoid can be referred to as a non-associativeordered semigroup, as the main di¤erence between an ordered semigroup and anordered AG-groupoid is the switching of an associative law. In this paper, wede ne the smallest left (right) ideals in an ordered AG-groupoid and use them tocharacterize a (2; 2)-regular class of a unitary ordered AG-groupoid along with itssemilattices and (2 ;2 _q)-fuzzy left (right) ideals. We also give the conceptof an ordered A*G**-groupoid and investigate its structural properties by usingthe generated ideals and (2 ;2 _q)-fuzzy left (right) ideals. These concepts willverify the existing characterizations and will help in achieving more generalizedresults in future works.
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28

Azeef Muhammed, P. A., and A. R. Rajan. "Cross-connections of the singular transformation semigroup." Journal of Algebra and Its Applications 17, no. 03 (2018): 1850047. http://dx.doi.org/10.1142/s0219498818500470.

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Cross-connection is a construction of regular semigroups using certain categories called normal categories which are abstractions of the partially ordered sets of principal left (right) ideals of a semigroup. We describe the cross-connections in the semigroup [Formula: see text] of all non-invertible transformations on a set [Formula: see text]. The categories involved are characterized as the powerset category [Formula: see text] and the category of partitions [Formula: see text]. We describe these categories and show how a permutation on [Formula: see text] gives rise to a cross-connection. Further, we prove that every cross-connection between them is induced by a permutation and construct the regular semigroups that arise from the cross-connections. We show that each of the cross-connection semigroups arising this way is isomorphic to [Formula: see text]. We also describe the right reductive subsemigroups of [Formula: see text] with the category of principal left ideals isomorphic to [Formula: see text]. This study sheds light into the more general theory of cross-connections and also provides an alternate way of studying the structure of [Formula: see text].
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29

Omidi, Saber, and Bijan Davvaz. "Convex ordered Gamma-semihypergroups associated to strongly regular relations." MATEMATIKA 33, no. 2 (2017): 227. http://dx.doi.org/10.11113/matematika.v33.n2.838.

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In this study, we introduce and investigate the notion of convex ordered Gamma-semihypergroups associated to strongly regular relations. Afterwards, we prove that if sigma is a strongly regular relation on a convex ordered Gamma-semihypergroup, then the quotient set is an ordered Gamma-sigma-semigroup. Also, some results on the product of convex ordered Gamma-semihypergroups are given. As an application of the results of this paper, the corresponding results of ordered semihypergroups are also obtained by moderate modifications.
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30

Steinberg, Benjamin. "FACTORIZATION THEOREMS FOR MORPHISMS OF ORDERED GROUPOIDS AND INVERSE SEMIGROUPS." Proceedings of the Edinburgh Mathematical Society 44, no. 3 (2001): 549–69. http://dx.doi.org/10.1017/s0013091599001017.

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AbstractAdapting the theory of the derived category to ordered groupoids, we prove that every ordered functor (and thus every inverse and regular semigroup homomorphism) factors as an enlargement followed by an ordered fibration. As an application, we obtain Lawson’s version of Ehresmann’s Maximum Enlargement Theorem, from which can be deduced the classical theory of idempotent-pure inverse semigroup homomorphisms and $E$-unitary inverse semigroups.AMS 2000 Mathematics subject classification: Primary 20M18; 20L05; 20M17
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31

Luangchaisri, Panuwat, and Thawhat Changphas. "Prime one-sided ideals in ordered semigroups." Quasigroups and Related Systems 32, no. 1(51) (2024): 49–57. https://doi.org/10.56415/qrs.v32.05.

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We prove that the following are equivalent: (1) an ordered semigroup S with zero and identity is right weakly regular; (2) (AA] = A for any right ideal A of S; (3) A \ I = (AI] for any right ideal A and two-sided ideal I of S; (4) B \ I (BI] for any bi-ideal B and two-sided ideal I of S; (5) B\I \A (BIA] for any bi-ideal B, right ideal A and two-sided ideal I of S; and prove that S is a fully prime right ordered semigroup if and only if S is right weakly regular and the set of all two-sided ideals of S is totally ordered.
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32

Saito, Tatsuhiko. "Naturally ordered regular semigroups with maximum inverses." Proceedings of the Edinburgh Mathematical Society 32, no. 1 (1989): 33–39. http://dx.doi.org/10.1017/s001309150000688x.

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Let S be a regular semigroup. An inverse subsemigroup S° of S is called an inverse transversal if S° contains a unique inverse of each element of S. An inverse transversal S° of S is called multiplicative if x°xyy° is an idempotent of S° for every x, y∈S, where x° denotes the unique inverse of x∈S in S°. In Section 1, we obtain a necessary and sufficient condition in order for inverse transversals to be multiplicative.
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33

Amjid, Venus, Faisal Yousafzai, and Kostaq Hila. "A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals." Advances in Fuzzy Systems 2018 (September 2, 2018): 1–8. http://dx.doi.org/10.1155/2018/8464295.

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An ordered AG-groupoid can be referred to as an ordered left almost semigroup, as the main difference between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we define the smallest one-sided ideals in an ordered AG-groupoid and use them to characterize a strongly regular class of a unitary ordered AG-groupoid along with its semilattices and fuzzy one-sided ideals. We also introduce the concept of an orderedAG⁎⁎⁎-groupoid and investigate its structural properties by using the generated ideals and fuzzy one-sided ideals. These concepts will verify the existing characterizations and will help in achieving more generalized results in future works.
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34

Nupo, Nuttawoot, and Sayan Panma. "Certain structural properties for Cayley regularity graphs of semigroups and their theoretical applications." AIMS Mathematics 8, no. 7 (2023): 16228–39. http://dx.doi.org/10.3934/math.2023830.

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<abstract><p>An element $ x $ in a semigroup is said to be regular if there exists an element $ y $ in the semigroup such that $ x = xyx $. The element $ y $ is said to be a regular part of $ x $. Define the Cayley regularity graph of a semigroup $ S $ to be a digraph with vertex set $ S $ and arc set containing all ordered pairs $ (x, y) $ such that $ y $ is a regular part of $ x $. In this paper, certain classes of Cayley regularity graphs such as complete digraphs, connected digraphs and equivalence digraphs are investigated. Furthermore, structural properties of the Cayley regularity graphs are theoretically applied to study perfect matchings of other algebraic graphs.</p></abstract>
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35

Tanyawong, Rossarin, Ratana Srithus, and Ronnason Chinram. "Regular subsemigroups of the semigroups of transformations preserving a fence." Asian-European Journal of Mathematics 09, no. 01 (2016): 1650003. http://dx.doi.org/10.1142/s1793557116500030.

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It is well-known that the transformation semigroup [Formula: see text] is regular, but their subsemigroups need not be. A fence is an ordered set that the order forms a path with alternating orientation. Consider [Formula: see text] as the base set of a fence [Formula: see text]. Two subsemigroups of [Formula: see text] are studied. Namely, the semigroup [Formula: see text] of all order-decreasing self-mappings of [Formula: see text] and the semigroup [Formula: see text] of all order-preserving self-mappings of [Formula: see text]. In this paper, we obtain that [Formula: see text] is a coregular subsemigroup of [Formula: see text]. A characterization of regular subsemigroups [Formula: see text] of [Formula: see text] is given, that is, [Formula: see text] is regular if and only if [Formula: see text]. Finally, we discuss the regularity of elements in [Formula: see text].
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36

Bhuniya, Anjan Kumar, and Kalyan Hansda. "On the subsemigroup generated by ordered idempotents of a regular semigroup." Discussiones Mathematicae - General Algebra and Applications 35, no. 2 (2015): 205. http://dx.doi.org/10.7151/dmgaa.1235.

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37

Blyth, T. S. "On the endomorphism semigroup of an ordered set." Glasgow Mathematical Journal 37, no. 2 (1995): 173–78. http://dx.doi.org/10.1017/s0017089500031074.

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M. E. Adams and Matthew Gould [1] have obtained a remarkable classification of ordered sets P for which the monoid End P of endomorphisms (i.e. isotone maps) is regular, in the sense that for every f є End P there exists g є End P such that fgf = f. They show that the class of such ordered sets consists precisely of(a) all antichains;(b) all quasi-complete chains;(c) all complete bipartite ordered sets (i.e. given non-zero cardinals α β an ordered set Kα,β of height 1 having α minimal elements and β maximal elements, every minimal element being less than every maximal element);(d) for a non-zero cardinal α the lattice Mα consisting of a smallest element 0, a biggest element 1, and α atoms;(e) for non-zero cardinals α, β the ordered set Nα,β of height 1 having α minimal elements and β maximal elements in which there is a unique minimal element α0 below all maximal elements and a unique maximal element β0 above all minimal elements (and no further ordering);(f) the six-element crown C6 with Hasse diagramA similar characterisation, which coincides with the above for sets of height at most 2 but differs for chains, was obtained by A. Ya. Aizenshtat [2].
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38

Umar, Abdullahi. "On the semigroups of order-decreasing finite full transformations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 120, no. 1-2 (1992): 129–42. http://dx.doi.org/10.1017/s0308210500015031.

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SynopsisLet Singn be the subsemigroup of singular elements of the full transformation semigroup on a totally ordered finite set with n elements. Let be the subsemigroup of all decreasing maps of Singn. In this paper it is shown that is a non-regular abundant semigroup with n − 1 -classes and . Moreover, is idempotent-generated and it is generated by the n(n − 1)/2 idempotents in J*n−1. LetandSome recurrence relations satisfied by J*(n, r) and sh (n, r) are obtained. Further, it is shown that sh (n, r) is the complementary signless (or absolute) Stirling number of the first kind.
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39

Karyati, K., A. Maman Abadi, and Musthofa. "The properties of the ordered bilinear form semigroup related to their regular elements." Journal of Physics: Conference Series 1321 (October 2019): 032126. http://dx.doi.org/10.1088/1742-6596/1321/3/032126.

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40

Sullivan, R. P. "Partial orders on linear transformation semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135, no. 2 (2005): 413–37. http://dx.doi.org/10.1017/s0308210500003942.

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Let V be any vector space and P(V) the set of all partial linear transformations defined on V, that is, all linear α: A → B, where A, B are subspaces of V. Then P(V) is a semigroup under composition, which is partially ordered by ⊆ (that is, α ⊆ β if and only if dom α ⊆ dom β and α = β | dom α). We compare this order with the so-called 'natural partial order' ≤ on P(V) and we determine their meet and join. We also describe all elements of P(V) that are minimal (or maximal) with respect to each of these four orders, and we characterize all elements that are 'compatible' with them. In addition, we answer similar questions for the semigroup T(V) consisting of all α ∈ P(V) whose domain equals V. Other orders have been defined by Petrich on any regular semigroup: three of them form a chain below ≤, and we show that two of these are equal on the semigroup P(V) and on the ring T(V). We also consider questions for these orders that are similar to those already mentioned
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41

SAGHAFI, ANAHITA. "On the L1-algebras of some compact totally ordered spaces." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 1 (1997): 173–84. http://dx.doi.org/10.1017/s0305004196001612.

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Let X be a compact totally ordered space made into a semigroup by the multiplication xy=max{x, y}. Suppose that there is a continuous regular Borel measure μ on X with supp μ=X. Then the space L1(μ) of μ-integrable functions becomes a Banach algebra when provided with convolution as multiplication. The second dual L1(μ)** therefore has two Arens multiplications, each making it a Banach algebra. We shall always consider L1(μ)** to have the first of these: if F, G∈L1(μ)** and F=w*−limi ϕi, G=w*−limj ψj, where (ϕi), (ψj) are bounded nets in L1(μ), thenformula here
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42

Matsuda, Ryuki. "Note on integral closures of semigroup rings." Tamkang Journal of Mathematics 31, no. 2 (2000): 137–44. http://dx.doi.org/10.5556/j.tkjm.31.2000.405.

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Let $S$ be a subsemigroup which contains 0 of a torsion-free abelian (additive) group. Then $S$ is called a grading monoid (or a $g$-monoid). The group $ \{s-s'|s,s'\in S\}$ is called the quotient group of $S$, and is denored by $q(S)$. Let $R$ be a commutative ring. The total quotient ring of $R$ is denoted by $q(R)$. Throught the paper, we assume that a $g$-monoid properly contains $ \{0\}$. A commutative ring is called a ring, and a non-zero-divisor of a ring is called a regular element of the ring. We consider integral elements over the semigroup ring $ R[X;S]$ of $S$ over $R$. Let $S$ be a $g$-monoid with quotient group $G$. If $ n\alpha\in S$ for an element $ \alpha$ of $G$ and a natural number $n$ implies $ \alpha\in S$, then $S$ is called an integrally closed semigroup. We know the following fact: ${\bf Theorem~1}$ ([G2, Corollary 12.11]). Let $D$ be an integral domain and $S$ a $g$-monoid. Then $D[X;S]$ is integrally closed if and only if $D$ is an integrally closed domain and $S$ is an integrally closed semigroup. Let $R$ be a ring. In this paper, we show that conditions for $R[X;S]$ to be integrally closed reduce to conditions for the polynomial ring of an indeterminate over a reduced total quotient ring to be integrally closed (Theorem 15). Clearly the quotient field of an integral domain is a von Neumann regular ring. Assume that $q(R)$ is a von Neumann regular ring. We show that $R[X;S]$ is integrally closed if and only if $R$ is integrally closed and $S$ is integrally closed (Theorem 20). Let $G$ be a $g$-monoid which is a group. If $R$ is a subring of the ring $T$ which is integrally closed in $T$, we show that $R[X;G]$ is integrally closed in $T[X;S]$ (Theorem 13). Finally, let $S$ be sub-$g$-monoid of a totally ordered abelian group. Let $R$ be a subring of the ring $T$ which is integrally closed in $T$. If $g$ and $h$ are elements of $T[X;S]$ with $h$ monic and $gh\in R[X;S]$, we show that $g\in R[X;S]$ (Theorem 24).
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43

Omidi, S., B. Davvaz, and K. Hila. "Characterizations of regular and intra-regular ordered $\Gamma$-semihypergroups in terms of bi-$\Gamma$-hyperideals." Carpathian Mathematical Publications 11, no. 1 (2019): 136–51. http://dx.doi.org/10.15330/cmp.11.1.136-151.

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The concept of $\Gamma$-semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of $\Gamma$-semigroups. In this paper, we study the notion of bi-$\Gamma$-hyperideals in ordered $\Gamma$-semihypergroups and investigate some properties of these bi-$\Gamma$-hyperideals. Also, we define and use the notion of regular ordered $\Gamma$-semihypergroups to examine some classical results and properties in ordered $\Gamma$-semihypergroups.
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44

Blyth, T. S., and G. A. Pinto. "Pointed principally ordered regular semigroups." Discussiones Mathematicae - General Algebra and Applications 36, no. 1 (2016): 101. http://dx.doi.org/10.7151/dmgaa.1243.

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45

Blyth, T. S., and M. H. Almeida Santos. "E-special Ordered Regular Semigroups." Communications in Algebra 43, no. 8 (2015): 3294–312. http://dx.doi.org/10.1080/00927872.2014.918987.

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46

Kehayopulu, Niovi, and Michael Tsingelis. "On Intra-regular Ordered Semigroups." Semigroup Forum 57, no. 1 (1998): 138–41. http://dx.doi.org/10.1007/pl00005962.

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47

Kehayopulu, Niovi. "On intra-regular ordered semigroups." Semigroup Forum 46, no. 1 (1993): 271–78. http://dx.doi.org/10.1007/bf02573571.

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48

Kehayopulu, Niovi, and Michael Tsingelis. "On Left Regular Ordered Semigroups." Southeast Asian Bulletin of Mathematics 25, no. 4 (2002): 609–15. http://dx.doi.org/10.1007/s100120200005.

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49

Khan, Asghar, Young Bae Jun та Muhammad Shabir. "𝒩-Fuzzy Ideals in Ordered Semigroups". International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–14. http://dx.doi.org/10.1155/2009/814861.

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We introduce the concept of𝒩-fuzzy left (right) ideals in ordered semigroups and characterize ordered semigroups in terms of𝒩-fuzzy left (right) ideals. We characterize left regular (right regular) and left simple (right simple) ordered semigroups in terms of𝒩-fuzzy left (𝒩-fuzzy right) ideals. The semilattice of left (right) simple semigroups in terms of𝒩-fuzzy left (right) ideals is discussed.
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50

Shahida Bashir and Xiankun Du. "Intra-regular and weakly regular ordered ternary semigroups." ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 13, no. 4 (2017): 539–51. http://dx.doi.org/10.30948/afmi.2017.13.4.539.

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