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Journal articles on the topic 'Commutative Ordered Ternary Semigroup'

Author: Grafiati

Published: 7 June 2025

Last updated: 17 July 2025

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1

Nakwan, Kansada, Panuwat Luangchaisri, and Thawhat Changphas. "Implicative Negatively Partially Ordered Ternary Semigroups." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 4180–94. https://doi.org/10.29020/nybg.ejpam.v17i4.5511.

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In this paper, we introduce and examine the notion of implicative negatively partially ordered ternary semigroups, for short implicative n.p.o. ternary semigroup, which include an element that serves as both the greatest element and the multiplicative identity. We study the notion of implicative homomorphisms between these ternary semigroups, and have that any implicativehomomorphism is a homomorphism. Let φ : T1→T2 be an implicative homomorphism from a commutative implicative n.p.o. ternary semigroup T1 onto T2. We construct a quotient commutative implicative n.p.o. ternary semigroup T1/ρKer

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2

Shinde, Dattatray N., Machchhindra T. Gophane, and Manish C. Agalave. "Ordered Pseudo-Ideals of An Ordered Ternary Semigroup." Indian Journal Of Science And Technology 18, no. 4 (2025): 281–86. https://doi.org/10.17485/ijst/v18i4.3500.

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Objectives: This research explores the concept of ordered pseudo-ideals in an ordered ternary semigroup 𝐺, which builds on the existing idea of pseudoideals in a semigroup. Methods: The investigation delves into some unique properties of ordered pseudo-ideals in an ordered ternary semigroup 𝐺. Findings: This study has established many sufficient conditions for (𝐿𝑀𝑁] to be an ordered pseudo-ideal of 𝐺 where 𝐿, 𝑀 and 𝑁 are non-empty subsets of 𝐺. Additionally, the study provides conditions for subsets (𝐿𝐵𝐵] and (𝐵𝐵𝐿] to be recognized as ordered left and right pseudo-ideals, respectively, as well

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3

Dattatray, N. Shinde, T. Gophane Machchhindra, and C. Agalave Manish. "Ordered Pseudo-Ideals of An Ordered Ternary Semigroup." Indian Journal of Science and Technology 18, no. 4 (2025): 281–86. https://doi.org/10.17485/IJST/v18i4.3500.

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<strong>Objectives:</strong> This research explores the concept of ordered pseudo-ideals in an ordered ternary semigroup 𝐺, which builds on the existing idea of pseudoideals in a semigroup. <strong>Methods:</strong> The investigation delves into some unique properties of ordered pseudo-ideals in an ordered ternary semigroup 𝐺. <strong>Findings:</strong> This study has established many sufficient conditions for (𝐿𝑀𝑁] to be an ordered pseudo-ideal of 𝐺 where 𝐿, 𝑀 and 𝑁 are non-empty subsets of 𝐺. Additionally, the study provides conditions for subsets (𝐿𝐵𝐵] and (𝐵𝐵𝐿] to

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4

Gophane, Machchhindra T., and Dattatray N. Shinde. "MAXIMAL AND MINIMAL PSEUDO SYMMETRIC IDEALS IN PARTIALLY ORDERED TERNARY SEMIGROUPS." South East Asian Journal of Mathematics and Mathematical Sciences 20, no. 02 (2024): 121–32. https://doi.org/10.56827/seajmms.2024.2002.9.

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We have introduced the notions of maximal and minimal pseudo symmetric ideals of a partially ordered ternary semigroup $T$ and studied their properties. We show that every maximal pseudo symmetric ideal of a commutative partially ordered ternary semigroup with identity is a prime pseudo symmetric ideal. We gave an example to show that the converse of this statement is not true.

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5

Nakwan, Kansada, Panuwat Luangchaisri, and Thawhat Changphas. "On Filters of Implicative Negatively Partially Ordered Ternary Semigroups." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5859. https://doi.org/10.29020/nybg.ejpam.v18i2.5859.

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In this paper, we study a special set in an implicative n.p.o.(negatively partially ordered) ternary semigroup, and prove that a filter can be represented by the union of such sets. Indeed, let $(T, [\,\,\,],\leq,[\,\,\,]^*)$ be an implicative n.p.o. ternary semigroup. For any $a, b\in T$, we define $$S(a,b):=\{c\in T \,:\, [aa[bbc]^*]^*=1\}.$$ We have the following:\begin{enumerate} \item [(1)] A non-empty subset $F$ of $T$ isa filter if and only if it satisfies the following conditions: \begin{enumerate} \item[(F3)] $1\in F$; \item[(F4)] for any $a, b,c \in T$, if $[abc]^*\in F$ and $a,b \in

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6

G, Ramesh, and Mahendran S. "Some Properties of Commutative Ternary Right Almost Semigroups." Indian Journal of Science and Technology 16, no. 45 (2023): 4255–66. https://doi.org/10.17485/IJST/v16i45.1937.

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Abstract <strong>Objective/Background:</strong> In this paper, the concept of commutative ternary right almost semigroups is introduced. The properties of ternary right almost semigroups and commutative ternary right almost semigroups are also discussed. Finally, regular only and the regularity are also explored in ternary right almost semigroups. <strong>Methods:</strong> Properties of ternary right almost semigroup have been employed to carry out this research work to obtain all the characterizations of commutative ternary right almost semigroups, regular and normal correspond

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7

Jantanan, Wichayaporn, Natee Raikham, and Ronnason Chinram. "On right bases of partially ordered ternary semigroups." Quasigroups and Related Systems 30, no. 2(48) (2023): 209–18. http://dx.doi.org/10.56415/qrs.v30.18.

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We investigate the results of a partially ordered ternary semigroup containing right bases and characterize when a non-empty subset of a partially ordered ternary semigroup is a right base. Moreover, we give a characterization of a right base of a partially ordered ternary semigroup to be a ternary subsemigroup and we show that the right bases of a partially ordered ternary semigroup have same cardinality. Finally, we show that the complement of the union of all right bases of a partially ordered ternary semigroup is a maximal proper left ideal.

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8

Andri, Andri, and Nasria Nacong. "KONDISI MINIMAL IDEAL KIRI TERURUT PADA SEMIGRUP TERNER TERURUT PARSIAL." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 15, no. 2 (2019): 280–87. http://dx.doi.org/10.22487/2540766x.2018.v15.i2.13225.

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Ternary semigroups 𝑇 is obtained from a nonempty set 𝑇 that given a mapping with a multiplication operation ternary that satisfied closed and associative properties. So, generally a ternary semigroup is an abstraction of a semigroup structure. Meanwhile, partially ordered ternary semigroups 𝑇 is an ordered semigroup 𝑇 that satisfies the properties for each 𝑎, 𝑏, 𝑐, 𝑑 ∈ 𝑇 if 𝑎 ≤ 𝑏 then (𝑎𝑐𝑑) ≤ (𝑏𝑐𝑑) and (𝑑𝑐𝑎) ≤ (𝑑𝑐𝑏). In a ternary semigroups there is also concept of left ideals. This study was conducted to examine the characteristics of ordered left ideals on partially ordered ternary semigroup

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9

Shinde, Dattatray, and Machchhindra Gophane. "On irreducible pseudo symmetric ideals of a partially ordered ternary semigroup." Quasigroups and Related Systems 30, no. 1(47) (2022): 169–80. http://dx.doi.org/10.56415/qrs.v30.15.

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In this paper, the concepts of irreducible and strongly irreducible pseudo symmetric ideals in a partially ordered ternary semigroup are introduced. We also studied some interesting properties of irreducible and strongly irreducible pseudo symmetric ideals of a partially ordered ternary semigroup and prove that the space of strongly irreducible pseudo symmetric ideals of a partially ordered ternary semigroup is topologized.

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10

Gophane, Machchhindra, and Dattatray Shinde. "On pseudo-ideals in partially ordered ternary semigroups." Quasigroups and Related Systems 32, no. 1(51) (2024): 41–48. https://doi.org/10.56415/qrs.v32.04.

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We study the properties of different types of pseudo-ideals of a partially ordered ternary semigroup and prove that the space of all strongly irreducible pseudoideals of a partially ordered ternary semigroup is a compact space.

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11

Pattinasarany, Noverly Cloren. "Ideal Dalam Semigrup Ternari Komutatif." Tensor: Pure and Applied Mathematics Journal 1, no. 2 (2020): 77–82. http://dx.doi.org/10.30598/tensorvol1iss2pp77-82.

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Algebra is a branch of mathematics that deals with mathematical objects (say, numbers with no known exact value), and uses symbols such as x and y to study them. In algebra, the properties possessed by the operations that can be performed on the object (think addition and multiplication) are studied, and then become "weapons" when we are faced with a problem related to that object. In the structure of algebra, there are many theories such as groups, abelian groups, and semigroups. In semigroups only use binary operations, this makes researchers want to make research on semigroups using ternary

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12

Kehayopulu, Niovi, and Michael Tsingelis. "Noetherian and Artinian ordered groupoids—semigroups." International Journal of Mathematics and Mathematical Sciences 2005, no. 13 (2005): 2041–51. http://dx.doi.org/10.1155/ijmms.2005.2041.

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Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids (semigroups). Noetherian ordered groupoids (semigroups) which are about to be introduced are particularly versatile. These satisfy a certain finiteness condition, namely, that every ideal of the ordered groupoid (semigroup) is finitely generated.

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13

Easdown, D., and W. D. Munn. "On semigroups with involution." Bulletin of the Australian Mathematical Society 48, no. 1 (1993): 93–100. http://dx.doi.org/10.1017/s0004972700015495.

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A semigroup S with an involution * is called a special involution semigroup if and only if, for every finite nonempty subset T of S,.It is shown that a semigroup is inverse if and only if it is a special involution semigroup in which every element invariant under the involution is periodic. Other examples of special involution semigroups are discussed; these include free semigroups, totally ordered cancellative commutative semigroups and certain semigroups of matrices. Some properties of the semigroup algebras of special involution semigroups are also derived. In particular, it is shown that t

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14

Widiastuti, Ratna Sari. "Radikal Prima Bi-Ideal Dalam Semiring Ternari." Jurnal Matematika 9, no. 2 (2019): 78. http://dx.doi.org/10.24843/jmat.2019.v09.i02.p113.

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A ternary semiring is an additive commutative semigroup with a ternary multiplication which satisfying some condition. This paper will be discuss about prime bi-ideal radikal in semiring ternary with definition and some theorem. If B is a bi-ideal in semiring ternary T, then radical prime bi-ideal of B in semiring ternary T is an intersection of all prime bi-ideal in semiring ternary T which containing B.

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15

Elliott, George A., and Jesper Villadsen. "Perforated Ordered K0-Groups." Canadian Journal of Mathematics 52, no. 6 (2000): 1164–91. http://dx.doi.org/10.4153/cjm-2000-049-9.

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AbstractA simple C*-algebra is constructed for which theMurray-von Neumann equivalence classes of projections, with the usual addition—induced by addition of orthogonal projections—form the additive semigroup{0, 2, 3, . . .}.(This is a particularly simple instance of the phenomenon of perforation of the ordered K0-group, which has long been known in the commutative case—for instance, in the case of the four-sphere—and was recently observed by the second author in the case of a simple C*-algebra.)

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16

Klep, Igor. "On Valuations, Places and Graded Rings Associated to ∗-Orderings." Canadian Mathematical Bulletin 50, no. 1 (2007): 105–12. http://dx.doi.org/10.4153/cmb-2007-010-4.

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AbstractWe study natural ∗-valuations, ∗-places and graded ∗-rings associated with ∗-ordered rings. We prove that the natural ∗-valuation is always quasi-Ore and is even quasi-commutative (i.e., the corresponding graded ∗-ring is commutative), provided the ring contains an imaginary unit. Furthermore, it is proved that the graded ∗-ring is isomorphic to a twisted semigroup algebra. Our results are applied to answer a question of Cimprič regarding ∗-orderability of quantum groups.

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17

Tsvetov, V. P. "SEMIGROUPS OF BINARY OPERATIONS AND MAGMA-BASED CRYPTOGRAPHY." Vestnik of Samara University. Natural Science Series 26, no. 1 (2020): 23–51. http://dx.doi.org/10.18287/2541-7525-2020-26-1-23-51.

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In this article, algebras of binary operations as a special case of finitary homogeneous relations algebrasare investigated. The tools of our study are based on unary and associative binary operations acting on theset of ternary relations. These operations are generated by the converse operation and the left-composition ofbinary relations. Using these tools, we are going to define special kinds of ternary relations that correspondto functions, injections, right- and left-total binary relations. Then we obtain criteria for these properties interms of ordered semigroups. Note, that there is an e

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18

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 (

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19

Blackmore, T. D. "Derivations from Totally Ordered Semigroup Algebras into their Duals." Canadian Mathematical Bulletin 40, no. 2 (1997): 133–42. http://dx.doi.org/10.4153/cmb-1997-016-9.

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AbstractFor a well-behaved measure μ, on a locally compact totally ordered set X, with continuous part μc, we make Lp (X, μc) into a commutative Banach bimodule over the totally ordered semigroup algebra Lp (X, μ), in such a way that the natural surjection from the algebra to the module is a bounded derivation. This gives rise to bounded derivations from Lp (X, μ) into its dual module and in particular shows that if μc is not identically zero then Lp (X, μ) is not weakly amenable. We show that all bounded derivations from L1 (X, μ) into its dual module arise in this way and also describe all b

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20

SHINDE, DATTATRAY, and MACHCHHINDRA GOPHANE. "On Prime Ideal Space of a Partially Ordered Ternary Semigroup." Creative Mathematics and Informatics 33, no. 1 (2024): 77–85. http://dx.doi.org/10.37193/cmi.2024.01.08.

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In this paper, we introduced the hull-kernel topology $\tau$ on the set $\mathcal P$ of prime ideals in a partially ordered ternary semigroup $T$ and investigated various topological properties of the structure space $(\mathcal P, \tau)$. We also obtained some useful results about compactness and connectedness of the set of all prime full ideals of $T$.

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21

Sheu, Albert Jeu-Liang. "A Cancellation Theorem for Modules Over the Group C*-Algebras of Certain Nilpotent Lie Groups." Canadian Journal of Mathematics 39, no. 2 (1987): 365–427. http://dx.doi.org/10.4153/cjm-1987-018-7.

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In recent years, there has been a rapid growth of the K-theory of C*-algebras. From a certain point of view, C*-algebras can be treated as “non-commutative topological spaces”, while finitely generated projective modules over them can be thought of as “non-commutative vector bundles”. The K-theory of C*-algebras [30] then generalizes the classical K-theory of topological spaces [1]. In particular, the K0-group of a unital C*-algebra A is the group “generated” by (or more precisely, the Grothendieck group of) the commutative semigroup of stable isomorphism classes of finitely generated projecti

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22

ROMANO, Daniel A. "Shift filters of quasi-ordered residuated system." Communications in Advanced Mathematical Sciences 5, no. 3 (2022): 1. http://dx.doi.org/10.33434/cams.1089222.

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The concept of residuated relational systems ordered under a quasi-order relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure $\mathfrak{A} = \langle A, \cdot, \rightarrow, 1, R \rangle$, where $(A,\cdot)$ is a commutative semigroup with the identity $1$ as the top element in this ordered monoid under a quasi-order $R$. In 2020, the author introduced and analyzed the concepts of filters in this type of algebraic structures. In addition to the previous, the author continued to investigate some of the types of filters in quasi-ordered residuated systems such as,

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23

Gutik, Oleg, Dušan Pagon, and Kateryna Pavlyk. "Congruences on bicyclic extensions of a linearly ordered group." Acta et Commentationes Universitatis Tartuensis de Mathematica 15, no. 2 (2020): 61–80. http://dx.doi.org/10.12697/acutm.2011.15.10.

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In the paper we study inverse semigroups B(G), B^+(G), \overline{B}(G) and \overline{B}^+(G) which are generated by partial monotone injective translations of a positive cone of a linearly ordered group G. We describe Green’s relations on the semigroups B(G), B^+(G), \overline{B}(G) and \overline{B}^+(G), their bands and show that they are simple, and moreover, the semigroups B(G) and B^+(G) are bisimple. We show that for a commutative linearly ordered group G all non-trivial congruences on the semigroup B(G) (and B^+(G)) are group congruences if and only if the group G is archimedean. Also we

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24

Wehrung, Friedrich. "The Universal Theory of Ordered Equidecomposability Types Semigroups." Canadian Journal of Mathematics 46, no. 5 (1994): 1093–120. http://dx.doi.org/10.4153/cjm-1994-062-3.

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AbstractWe prove that a commutative preordered semigroup embeds into the space of all equidecomposability types of subsets of some set equipped with a group action (in short, a full type space) if and only if it satisfies the following axioms: (i) (⩝x,y) (x ≤ x + y); (ii) (⩝x,y)((x ≤ y and y ≤ x) ⇒ x = y); (iii) (⩝x,y,u, v)((x + u ≤ y + u and u ≤ v) ⩝ x + v ≤ y ≤ v); (iv) (⩝x, u, V)((x + u = u and u ≤ v) ⇒ x + v = v); (v) (⩝x,y)(mx ≤ my ⇒ x ≤ y) (all m ∊ Ν \ {0}). Furthermore, such a structure can always be embedded into a reduced power of the space Τ of nonempty initial segments of + with rat

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25

Bunina, E. I., and P. P. Semenov. "Automorphisms of the semigroup of invertible matrices with nonnegative elements over commutative partially ordered rings." Journal of Mathematical Sciences 162, no. 5 (2009): 633–55. http://dx.doi.org/10.1007/s10958-009-9650-5.

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26

Bunina, E. I. "Automorphisms of the semigroup of nonnegative invertible matrices of order two over partially ordered commutative rings." Mathematical Notes 91, no. 1-2 (2012): 3–11. http://dx.doi.org/10.1134/s0001434612010014.

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27

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

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28

Tsarkov, O. I. "Endomorphisms of the Semigroup G2(r) Over Partially Ordered Commutative Rings Without Zero Divisors and with 1/2." Journal of Mathematical Sciences 201, no. 4 (2014): 534–51. http://dx.doi.org/10.1007/s10958-014-2010-0.

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29

Gupta, Vikash Kumar, and Balasubramaniam Jayaram. "On the Pecking Order Between Those of Mitsch and Clifford." Mathematica Slovaca 73, no. 3 (2023): 565–82. http://dx.doi.org/10.1515/ms-2023-0042.

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ABSTRACT Order-theoretic explorations of algebraic structures are known to lead to hitherto hidden insights. Two such relations that have stood out are those of Mitsch and Clifford – the former for the generality in its application and the latter for the insights it offers. In this work, our motivation is to study the converse: we want to explore the extent of the utility of Mitsch’s order and the applicability of Clifford’s order. Firstly, we show that if the Mitsch’s poset is either bounded or a chain, arguably a richer order theoretic structure, the semigroup reduces to one of a simple band

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30

Zhuchok, A. V. "The least dimonoid congruences on relatively free trioids." Matematychni Studii 57, no. 1 (2022): 23–31. http://dx.doi.org/10.30970/ms.57.1.23-31.

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When Loday and Ronco studied ternary planar trees, they introduced types of algebras,called trioids and trialgebras. A trioid is a nonempty set equipped with three binary associativeoperations satisfying additional eight axioms relating these operations, while a trialgebra is justa linear analog of a trioid. If all operations of a trioid (trialgebra) coincide, we obtain the notionof a semigroup (associative algebra), and if two concrete operations of a trioid (trialgebra)coincide, we obtain the notion of a dimonoid (dialgebra) and so, trioids (trialgebras) are ageneralization of semigroups (as

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31

Kehayopulu, Niovi, and Michael Tsingelis. "Semigroup actions on ordered groupoids." Mathematica Slovaca 63, no. 1 (2013). http://dx.doi.org/10.2478/s12175-012-0080-3.

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AbstractIn this paper we prove that if S is a commutative semigroup acting on an ordered groupoid G, then there exists a commutative semigroup S̃ acting on the ordered groupoid G̃:=(G × S)/ρ̄ in such a way that G is embedded in G̃. Moreover, we prove that if a commutative semigroup S acts on an ordered groupoid G, and a commutative semigroup S̄ acts on an ordered groupoid Ḡ in such a way that G is embedded in S̄, then the ordered groupoid G̃ can be also embedded in Ḡ. We denote by ρ̄ the equivalence relation on G × S which is the intersection of the quasi-order ρ (on G × S) and its inverse ρ −

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32

Kar, S., A. Roy, and I. Dutta. "Ordered power ternary semigroups." Asian-European Journal of Mathematics, December 24, 2021. http://dx.doi.org/10.1142/s1793557122501807.

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We consider a power ternary semigroup [Formula: see text] associated with a ternary semigroup [Formula: see text] and study some properties of [Formula: see text] by using the corresponding properties of [Formula: see text]. After that we study the notion of ordered power ternary semigroup and our main aim is to establish some interconnection between the properties of a ternary semigroup [Formula: see text] and the associated ordered ternary semigroup [Formula: see text].

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33

Bunina, E., and K. Sosov. "Endomorphisms of the Semigroup of Nonnegative Invertible Matrices of Order Two Over Commutative Ordered Rings." Journal of Mathematical Sciences, February 18, 2023. http://dx.doi.org/10.1007/s10958-023-06293-5.

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