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Journal articles on the topic '-regular semigroups'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Luo, Xiao Qiang. "Π^*-Regular Semigroups". Bulletin of Mathematical Sciences and Applications 1 (серпень 2012): 46–51. http://dx.doi.org/10.18052/www.scipress.com/bmsa.1.46.

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2

Ibrahim, Abudulkarim, Chidozie Udeogu, and Babagana Ibrahim Bukar. "On Some Classes of Regular Semigroups." International Journal of Development Mathematics (IJDM) 1, no. 3 (2024): 126–30. http://dx.doi.org/10.62054/ijdm/0103.09.

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In this paper we study and analyze the relationships between some special classes of regular semigroups, namely: Generalized inverse semigroups, Orthodox semigroups and locally inverse semigroups based on their idempotent properties. We then use an example to prove that every locally inverse semigroup is not a generalized inverse semigroup, thus validating the statement; “A generalized inverse semigroup has the property of being locally inverse. However, not every locally inverse semigroup is a generalized inverse semigroup.”

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3

Istikaanah, Najmah, Ari Wardayani, Renny Renny, Ambar Sari Nurahmadhani, and Agustini Tripena Br Sb. "SEMIGRUP REGULER DAN SIFAT-SIFATNYA." Jurnal Ilmiah Matematika dan Pendidikan Matematika 13, no. 2 (2021): 71. http://dx.doi.org/10.20884/1.jmp.2021.13.2.4968.

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This article discusses some properties of regular semigroups. These properties are especially concerned with the relation of the regular semigroups to ideals, subsemigroups, groups, idempoten semigroups and invers semigroups. In addition, this paper also discusses the Cartesian product of two regular semigroups.  Keywords:ideal, idempoten semigroup, inverse semigroup, regular semigroup, subsemigroup.

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4

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 princi

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5

Wang, Shoufeng. "On E-semiabundant semigroups with a multiplicative restriction transversal." Studia Scientiarum Mathematicarum Hungarica 55, no. 2 (2018): 153–73. http://dx.doi.org/10.1556/012.2018.55.2.1374.

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Multiplicative inverse transversals of regular semigroups were introduced by Blyth and McFadden in 1982. Since then, regular semigroups with an inverse transversal and their generalizations, such as regular semigroups with an orthodox transversal and abundant semigroups with an ample transversal, are investigated extensively in literature. On the other hand, restriction semigroups are generalizations of inverse semigroups in the class of non-regular semigroups. In this paper we initiate the investigations of E-semiabundant semigroups by using the ideal of "transversals". More precisely, we fir

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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

Yuan, Zhiling, and K. P. Shum. "$\widetilde{\cal H}$-Supercryptogroups Having Regular Band Congruence." Algebra Colloquium 16, no. 04 (2009): 709–20. http://dx.doi.org/10.1142/s1005386709000674.

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We consider a generalized superabundant semigroup within the class of semiabundant semigroups, called a supercryptogroup since it is an analogy of a cryptogroup in the class of regular semigroups. We prove that a semigroup S is an [Formula: see text]-regular supercryptogroup if and only if S can be expressed as a refined semilattice of completely [Formula: see text]-simple semigroups. Some results on regular cryptogroups are extended to [Formula: see text]-regular supercryptogroups. Some results on superabundant semigroups are also generalized.

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8

Lawson, Mark V. "Rees matrix covers for a class of abundant semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 107, no. 1-2 (1987): 109–20. http://dx.doi.org/10.1017/s0308210500029383.

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SynopsisRecently considerable attention has been paid to the study of locally inverse regular semigroups. McAlister [14] obtained a description of such semigroups as locally isomorphic images of regular Rees matrix semigroups over an inverse semigroup. The class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic analogue of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP rings are abundant. The aim of this paper is to show how the structure

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9

El-Qallali, Abdulsalam. "Left regular bands of groups of left quotients." Glasgow Mathematical Journal 33, no. 1 (1991): 29–40. http://dx.doi.org/10.1017/s0017089500008004.

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In this paper we characterize semigroups S which have a semigroup Q of left quotients, where Q is an ℛ-unipotent semigroup which is a band of groups. Recall that an ℛ-unipotent (or left inverse) semigroup S is one in which every ℛ-class contains a unique idempotent. It is well-known that any ℛ-unipotent semigroup 5 is a regular semigroup in which the set of idempotents is a left regular band in that efe = ef for any idempotents e, fin S. ℛ-unipotent semigroups were studied by several authors, see for example [1] and [13].Bailes [1]characterized ℛ-unipotent semigroups which are bands of groups.

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10

Tóth, Csaba. "Right regular triples of semigroups." Quasigroups and Related Systems 31, no. 2(50) (2024): 293–304. https://doi.org/10.56415/qrs.v31.23.

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Let M(S; Λ; P) denote a Rees I × Λ matrix semigroup without zero over a semigroup S, where I is a singleton. If θS denotes the kernel of the right regular representation of a semigroup S, then a triple A, B, C of semigroups is said to be right regular, if there are mappings A P←− B and B P 0 −→ C such that M(A; B; P)/θM(A;B;P ) ∼= M(C; B; P 0 ). In this paper we examine right regular triples of semigroups.

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11

KANTOROVITZ, SHMUEL. "GENERATORS OF REGULAR SEMIGROUPS." Glasgow Mathematical Journal 50, no. 1 (2008): 47–53. http://dx.doi.org/10.1017/s0017089507003916.

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AbstractA regular semigroup (cf. [4, p. 38]) is a C0-semigroup T(⋅) that has an extension as a holomorphic semigroup W(⋅) in the right halfplane $\Bbb C^+$, such that ||W(⋅)|| is bounded in the ‘unit rectangle’ Q:=(0, 1]× [−1, 1]. The important basic facts about a regular semigroup T(⋅) are: (i) it possesses a boundary groupU(⋅), defined as the limit lims → 0+W(s+i⋅) in the strong operator topology; (ii) U(⋅) is a C0-group, whose generator is iA, where A denotes the generator of T(⋅); and (iii) W(s+it)=T(s)U(t) for all s+it ∈$\Bbb C^+$ (cf. Theorems 17.9.1 and 17.9.2 in [3]). The following con

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12

Munn, W. D. "Congruence-free regular semigroups." Proceedings of the Edinburgh Mathematical Society 28, no. 1 (1985): 113–19. http://dx.doi.org/10.1017/s0013091500003254.

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A semigroup is said to be congruence-free if and only if its only congruences are the universal relation and the identical relation. Congruence-free inverse semigroups were studied by Baird [2], Trotter [19], Munn [15,16] and Reilly [18]. In addition, results on congruence-free regular semigroups have been obtained by Trotter [20], Hall [4] and Howie [7].

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13

NI, XIANGFEI, and HAIZHOU CHAO. "REGULAR SEMIGROUPS WITH NORMAL IDEMPOTENTS." Journal of the Australian Mathematical Society 103, no. 1 (2017): 116–25. http://dx.doi.org/10.1017/s1446788717000088.

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In this paper, we investigate regular semigroups that possess a normal idempotent. First, we construct a nonorthodox nonidempotent-generated regular semigroup which has a normal idempotent. Furthermore, normal idempotents are described in several different ways and their properties are discussed. These results enable us to provide conditions under which a regular semigroup having a normal idempotent must be orthodox. Finally, we obtain a simple method for constructing all regular semigroups that contain a normal idempotent.

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14

Kelarev, A. V. "The regular radical of semigroup rings of commutative semigroups." Glasgow Mathematical Journal 34, no. 2 (1992): 133–41. http://dx.doi.org/10.1017/s001708950000865x.

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A description of regular group rings is well known (see [12]). Various authors have considered regular semigroup rings (see [17], [8], [10], [11], [4]). These rings have been characterized for many important classes of semigroups, although the general problem turns out to be rather difficult and still has not got a complete solution. It seems natural to describe the regular radical in semigroup rings for semigroups of the classes mentioned. In [10], the regular semigroup rings of commutative semigroups were described. The aim of the present paper is to characterize the regular radical ρ(R[S])

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15

Guo, Xiaojiang, K. P. Shum, and Yongqian Zhu. "REES MATRIX COVERS FOR TIGHT ABUNDANT SEMIGROUPS." Asian-European Journal of Mathematics 03, no. 03 (2010): 409–25. http://dx.doi.org/10.1142/s1793557110000398.

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Rees matrix covers for regular semigroups were first studied by McAlister in 1984. Lawson extended McAlister's results to abundant semigroups in 1987. We consider here a semigroup whose set of regular elements forms a subsemigroup, named tight semigroups. In this paper, it is proved that an abundant semigroup is tight and locally E-solid if and only if it is an F-local isomorphic image of an abundant Rees matrix semigroup [Formula: see text] over a tight E-solid abundant semigroup T, where the entries of the sandwich matrix P of [Formula: see text] are regular elements of T. Our results enrich

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16

Et. al., Dr D. Mrudula Devi. "A characterization of Commutative Semigroups." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (2021): 5150–55. http://dx.doi.org/10.17762/turcomat.v12i3.2065.

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This paper deals with some results on commutative semigroups. We consider (s,.) is externally commutative right zero semigroup is regular if it is intra regular and (s,.) is externally commutative semigroup then every inverse semigroup is u – inverse semigroup. We will also prove that if (S,.) is a H - semigroup then weakly cancellative laws hold in H - semigroup. In one case we will take (S,.) is commutative left regular semi group and we will prove that (S,.) is ∏ - inverse semigroup. We will also consider (S,.) is commutative weakly balanced semigroup and then prove every left (right) regul

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17

Lawson, M. V. "Enlargements of regular semigroups." Proceedings of the Edinburgh Mathematical Society 39, no. 3 (1996): 425–60. http://dx.doi.org/10.1017/s001309150002321x.

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We introduce a class of regular extensions of regular semigroups, called enlargements; a regular semigroup T is said to be an enlargement of a regular subsemigroup S if S = STS and T = TST. We show that S and T have many properties in common, and that enlargements may be used to analyse a number of questions in regular semigroup theory.

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18

Pastijn, F. J., and Mario Petrich. "Rees matrix semigroups over inverse semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 102, no. 1-2 (1986): 61–90. http://dx.doi.org/10.1017/s0308210500014499.

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SynopsisA Rees matrix semigroup over an inverse semigroup contains a greatest regular subsemigroup. The regular semigroups obtained in this manner are abstractly characterized here. The greatest completely simple homomorphic image and the idempotent generated part of such semigroups are investigated. Rectangular bands of semilattices of groups and some special cases are characterized in several ways.

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19

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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20

Thomas, Julie, K. Indhira, and V. M. Chandrasekaran. "A Study on Regular Semigroups and its Idempotents." International Journal of Engineering & Technology 7, no. 4.10 (2018): 511. http://dx.doi.org/10.14419/ijet.v7i4.10.21214.

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An idempotent of a semigroup T is an element e in T such that In many semigroups, idempotents can be recognized easily. Thus it plays an important role in the structure of semigroups especially on regular semigroups. This article reviews about some research work done about the structure of regular semigroups with a special emphasis on its idempotents.

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21

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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22

Kong, Xiangzhi, Zhiling Yuan, and K. P. Shum. "A Structure Theorem of Regular ${\cal H}^\sharp$-Cryptographs." Algebra Colloquium 15, no. 04 (2008): 653–66. http://dx.doi.org/10.1142/s100538670800062x.

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A new set of generalized Green relations is given in studying the [Formula: see text]-abundant semigroups. By using the generalized strong semilattice of semigroups recently developed by the authors, we show that an [Formula: see text]-abundant semigroup is a regular [Formula: see text]-cryptograph if and only if it is an [Formula: see text]-strong semilattice of completely [Formula: see text]-simple semigroups. This result not only extends the well known result of Petrich and Reilly from the class of completely regular semigroups to the class of semiabundant semigroups, but also generalizes a

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23

Auinger, K., J. Doyle, and P. R. Jones. "On existence varieties of locally inverse semigroups." Mathematical Proceedings of the Cambridge Philosophical Society 115, no. 2 (1994): 197–217. http://dx.doi.org/10.1017/s0305004100072042.

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AbstractA locally inverse semigroup is a regular semigroup S with the property that eSe is inverse for each idempotent e of S. Motivated by natural examples such as inverse semigroups and completely simple semigroups, these semigroups have been the subject of deep structure-theoretic investigations. The class ℒ ℐ of locally inverse semigroups forms an existence variety (or e-variety): a class of regular semigroups closed under direct products, homomorphic images and regular subsemigroups. We consider the lattice ℒ(ℒℐ) of e-varieties of such semigroups. In particular we investigate the operatio

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24

Petrich, Mario. "Embedding Regular Semigroups into Idempotent Generated Ones." Algebra Colloquium 17, no. 02 (2010): 229–40. http://dx.doi.org/10.1142/s1005386710000246.

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Any semigroup S can be embedded into a semigroup, denoted by ΨS, having some remarkable properties. For general semigroups there is a close relationship between local submonoids of S and of ΨS. For a number of usual semigroup properties [Formula: see text], we prove that S and ΨS simultaneously satisfy [Formula: see text] or not. For a regular semigroup S, the relationship of S and ΨS is even closer, especially regarding the natural partial order and Green's relations; in addition, every element of ΨS is a product of at most four idempotents. For completely regular semigroups S, the relationsh

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PETRICH, MARIO. "COMPLETELY REGULAR MONOIDS WITH TWO GENERATORS." Journal of the Australian Mathematical Society 90, no. 2 (2011): 271–87. http://dx.doi.org/10.1017/s1446788711001108.

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AbstractWe classify semigroups in the title according to whether they have a finite or an infinite number ofℒ-classes or ℛ-classes. For each case, we provide a concrete construction using Rees matrix semigroups and their translational hulls. An appropriate relatively free semigroup is used to complete the classification. All this is achieved by first treating the special case in which one of the generators is idempotent. We conclude by a discussion of a possible classification of 2-generator completely regular semigroups.

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26

Gu, Ze. "The Relationship between E -Semigroups and R -Semigroups." Journal of Mathematics 2023 (April 17, 2023): 1–3. http://dx.doi.org/10.1155/2023/3087790.

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A semigroup is called an E -semigroup ( R -semigroup) if the set of all idempotents (the set of all regular elements) forms a subsemigroup. In this paper, we introduce the concept of V -semigroups and establish the relationship between the three classes of semigroups.

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27

Tamilarasi, A. "Idempotent-separating extensions of regular semigroups." International Journal of Mathematics and Mathematical Sciences 2005, no. 18 (2005): 2945–75. http://dx.doi.org/10.1155/ijmms.2005.2945.

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For a regular biordered setE, the notion ofE-diagram and the associated regular semigroup was introduced in our previous paper (1995). Given a regular biordered setE, anE-diagram in a categoryCis a collection of objects, indexed by the elements ofEand morphisms ofCsatisfying certain compatibility conditions. With such anE-diagramAwe associate a regular semigroupRegE(A)havingEas its biordered set of idempotents. This regular semigroup is analogous to automorphism group of a group. This paper provides an application ofRegE(A)to the idempotent-separating extensions of regular semigroups. We intro

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28

Lawson, M. V. "Abundant Rees matrix semigroups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 1 (1987): 132–42. http://dx.doi.org/10.1017/s1446788700034017.

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AbstractThe class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic counterparts of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP-rings are abundant. In this paper we investigate the properties of Rees matrix semigroups over abundant semigroups. Some of our results generalise McAlister's work on regular Rees matrix semigroups.

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29

Guo, Xiaojiang, and Lin Chen. "Semigroup algebras of finite ample semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 2 (2012): 371–89. http://dx.doi.org/10.1017/s0308210510000715.

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An adequate semigroup S is called ample if ea = a(ea)* and ae = (ae)†a for all a ∈ S and e ∈ E(S). Inverse semigroups are exactly those ample semigroups that are regular. After obtaining some characterizations of finite ample semigroups, it is proved that semigroup algebras of finite ample semigroups have generalized triangular matrix representations. As applications, the structure of the radicals of semigroup algebras of finite ample semigroups is obtained. In particular, it is determined when semigroup algebras of finite ample semigroup are semiprimitive.

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30

Szendrei, Mária B. "Extensions of regular orthogroups by groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 59, no. 1 (1995): 28–60. http://dx.doi.org/10.1017/s1446788700038465.

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AbstractA common generalization of the author's embedding theorem concerning the E-unitary regular semigroups with regular band of idempotents, and Billhardt's and Ismaeel's embedding theorem on the inverse semigroups, the closure of whose set of idempotents is a Clifford semigroup, is presented. We prove that each orthodox semigroup with a regular band of idempotents, which is an extension of an orthogroup K by a group, can be embedded into a semidirect product of an orthogroup K′ by a group, where K′ belongs to the variety of orthogroups generated by K. The proof is based on a criterion of e

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31

Bonzini, C., A. Cherubini та B. Piochi. "The Least Commutative Congruence on a simple regular ω-semigroup". Glasgow Mathematical Journal 32, № 1 (1990): 13–23. http://dx.doi.org/10.1017/s0017089500009022.

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Piochi in [10] gives a description of the least commutative congruence γ of an inverse semigroup in terms of congruence pairs and generalizes to inverse semigroups the notion of solvability. The object of this paper is to give an explicit construction of λ for simple regular ω-semigroups exploiting the work of Baird on congruences on such semigroups. Moreover the connection between the solvability classes of simple regular ω-semigroups and those of their subgroups is studied.

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Guo, Junying, and Xiaojiang Guo. "Self-injectivity of semigroup algebras." Open Mathematics 18, no. 1 (2020): 333–52. http://dx.doi.org/10.1515/math-2020-0023.

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Abstract It is proved that for an IC abundant semigroup (a primitive abundant semigroup; a primitively semisimple semigroup) S and a field K, if K 0[S] is right (left) self-injective, then S is a finite regular semigroup. This extends and enriches the related results of Okniński on self-injective algebras of regular semigroups, and affirmatively answers Okniński’s problem: does that a semigroup algebra K[S] is a right (respectively, left) self-injective imply that S is finite? (Semigroup Algebras, Marcel Dekker, 1990), for IC abundant semigroups (primitively semisimple semigroups; primitive ab

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33

Ćirić, Miroslav, and Stojan Bogdanović. "Strong bands of groups of left quotients." Glasgow Mathematical Journal 38, no. 2 (1996): 237–42. http://dx.doi.org/10.1017/s0017089500031499.

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An interesting concept of semigroups (and also rings) of (left) quotients, based on the notion of group inverse in a semigroup, was developed by J. B. Fountain, V. Gould and M. Petrich, in a series of papers (see [5]-[12]). Among the most interesting are semigroups having a semigroup of (left) quotients that is a union of groups. Such semigroups have been widely studied. Recall from [3] that a semigroup has a group of left quotients if and only if it is right reversible and cancellative. A more general result was obtained by V. Gould [10]. She proved that a semigroup has a semilattice of group

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34

Albayrak, Barış, Didem Yeşil, and Didem Karalarlioğlu Camci. "The Source of Semiprimeness of Semigroups." Journal of Mathematics 2021 (June 1, 2021): 1–8. http://dx.doi.org/10.1155/2021/4659756.

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In this study, we define new semigroup structures using the set S S = a ∈ S | a S a = 0 which is called the source of semiprimeness for a semigroup S with zero element. S S − idempotent semigroup, S S − regular semigroup, S S − reduced semigroup, and S S − nonzero divisor semigroup which are generalizations of idempotent, regular, reduced, and nonzero divisor semigroups in semigroup theory are investigated, and their basic properties are determined. In addition, we adapt some well-known results in semigroup theory to these new semigroups.

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35

Guo, Junying, and Xiaojiang Guo. "Algebras of right ample semigroups." Open Mathematics 16, no. 1 (2018): 842–61. http://dx.doi.org/10.1515/math-2018-0075.

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AbstractStrict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In particular, it is proved that any algebra of finite right ample semigroups has a generalized upper triangular matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. As its application, we determine when an alge

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36

Auinger, Karl. "Bifree objects in e-varieties of strict orthodox semigroups and the lattice of strict orthodox *-semigroup varieties." Glasgow Mathematical Journal 35, no. 1 (1993): 25–37. http://dx.doi.org/10.1017/s0017089500009538.

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For regular semigroups, the appropriate analogue of the concept of a variety seems to be that of an e(xistence)-variety, developed by Hall [6,7,8]. A class V of regular semigroups is an e-variety if it is closed under taking direct products, regular subsemigroups and homomorphic images. For orthodox semigroups, this concept has been introduced under the term “bivariety” by Kaďourek and Szendrei [12]. Hall showed that the collection of all e-varieties of regular semigroups forms a complete lattice under inclusion. Further, he proved a Birkhoff-type theorem: each e-variety is determined by a set

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37

Blyth, T. S., Emília Giraldes, and M. Paula O. Marques-Smith. "Associate subgroups of orthodox semigroups." Glasgow Mathematical Journal 36, no. 2 (1994): 163–71. http://dx.doi.org/10.1017/s0017089500030706.

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A unit regular semigroup [1, 4] is a regular monoid S such that H1 ∩ A(x) ≠ Ø for every xɛS, where H1, is the group of units and A(x) = {y ɛ S; xyx = x} is the set of associates (or pre-inverses) of x. A uniquely unit regular semigroupis a regular monoid 5 such that |H1 ∩ A(x)| = 1. Here we shall consider a more general situation. Specifically, we consider a regular semigroup S and a subsemigroup T with the property that |T ∩ A(x) = 1 for every x ɛ S. We show that T is necessarily a maximal subgroup Hα for some idempotent α. When Sis orthodox, α is necessarily medial (in the sense that x = xαx

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38

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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39

Bonzini, C., та A. Cherubini. "Modularity of the lattice of congruences of a regular ω-semigroup". Proceedings of the Edinburgh Mathematical Society 33, № 3 (1990): 405–17. http://dx.doi.org/10.1017/s0013091500004831.

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In this paper a characterization of the regular ω-semigroups whose congruence lattice is modular is given. The characterization obtained for such semigroups generalizes the one given by Munn for bisimple ω-semigroups and completes a result of Baird dealing with the modularity of the sublattice of the congruence lattice of a simple regular ω-semigroup consisting of congruences which are either idempotent separating or group congruences.

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40

Byleen, Karl. "Embedding any countable semigroup without idempotents in a 2-generated simple semigroup without idempotents." Glasgow Mathematical Journal 30, no. 2 (1988): 121–28. http://dx.doi.org/10.1017/s0017089500007126.

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Although the classes of regular simple semigroups and simple semigroups without idempotents are evidently at opposite ends of the spectrum of simple semigroups, their theories involve some interesting connections. Jones [5] has obtained analogues of the bicyclic semigroup for simple semigroups without idempotents. Megyesi and Pollák [7] have classified all combinatorial simple principal ideal semigroups on two generators, showing that all are homomorphic images of one such semigroup Po which has no idempotents.

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41

Goberstein, Simon M. "Correspondences of completely regular semigroups and -isomorphisms of semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 3 (1995): 625–37. http://dx.doi.org/10.1017/s0308210500032728.

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A correspondence of a semigroup S is any subsemigroup of S × S, and the set of all correspondences of S, with the operations of composition and involution and the relation of set-theoretic inclusion, forms the bundle of correspondences of S, denoted by (S). For semigroups S and T, any isomorphism of (S) onto (T) is called a -isomorphism of S upon T. Similar notion can be introduced for other types of algebras and in the general frame of category theory. The principal goal of this paper is to study -isomorphisms of completely regular semigroups (that is, unions of groups) and of one other inter

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42

Liaqat, Iqra, and Wajeeha Younas. "SOME IMPORTANT APPLICATIONS OF SEMIGROUPS." Journal of Mathematical Sciences & Computational Mathematics 2, no. 2 (2021): 317–21. http://dx.doi.org/10.15864/jmscm.2210.

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This Paper deals with the some important applications of semigroups in general and regular semigroups in particular.The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata via the syntactic monoid. In probability theory, semigroups are associated with Markov process. In section 2 we have seen different areas of applications of semigroups. We identified some Applications in biology, Partial Differential equation, Formal Languages etc whose semigroup structures are

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Worawiset, S., and J. Koppitz. "Endomorphisms of Clifford semigroups with injective structure homomorphisms." Algebra and Discrete Mathematics 30, no. 2 (2020): 290–304. http://dx.doi.org/10.12958/adm1543.

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In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is completely regular then the corresponding semilattice has at most two elements. We characterize all Clifford semigroups Gα∪Gβ (α>β) with an injective structure homomorphism, where Gα has no proper subgroup, such that the endomorphism monoid is completely regular. In particular, we consider the case t

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44

Wang, Qiumei, Jianming Zhan, and R. A. Borzooei. "A study on soft rough semigroups and corresponding decision making applications." Open Mathematics 15, no. 1 (2017): 1400–1413. http://dx.doi.org/10.1515/math-2017-0119.

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Abstract In this paper, we study a kind of soft rough semigroups according to Shabir’s idea. We define the upper and lower approximations of a subset of a semigroup. According to Zhan’s idea over hemirings, we also define a kind of new C-soft sets and CC-soft sets over semigroups. In view of this theory, we investigate the soft rough ideals (prime ideals, bi-ideals, interior ideals, quasi-ideals, regular semigroups). Finally, we give two decision making methods: one is for looking a best a parameter which is to the nearest semigroup, the other is to choose a parameter which keeps the maximum r

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45

Kong, Xiangzhi, and K. P. Shum. "Completely Regular Semigroups with Generalized Strong Semilattice Decompositions." Algebra Colloquium 12, no. 02 (2005): 269–80. http://dx.doi.org/10.1142/s100538670500026x.

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The concept of ρG-strong semilattice of semigroups is introduced. By using this concept, we study Green's relation ℋ on a completely regular semigroup S. Necessary and sufficient conditions for S/ℋ to be a regular band or a right quasi-normal band are obtained. Important results of Petrich and Reilly on regular cryptic semigroups are generalized and enriched. In particular, characterization theorems of regular cryptogroups and normal cryptogroups are obtained.

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Ren, Xueming, Qingyan Yin та K. P. Shum. "On Uσ-Abundant Semigroups". Algebra Colloquium 19, № 01 (2012): 41–52. http://dx.doi.org/10.1142/s100538671200003x.

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A U-abundant semigroup whose subset U satisfies a permutation identity is said to be Uσ-abundant. In this paper, we consider the minimum Ehresmann congruence δ on a Uσ-abundant semigroup and explore the relationship between the category of Uσ-abundant semigroups (S,U) and the category of Ehresmann semigroups (S,U)/δ. We also establish a structure theorem of Uσ-abundant semigroups by using the concept of quasi-spined product of semigroups. This generalizes a result of Yamada for regular semigroups in 1967 and a result of Guo for abundant semigroups in 1997.

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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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AUINGER, K., and T. E. HALL. "REPRESENTATIONS OF SEMIGROUPS BY TRANSFORMATIONS AND THE CONGRUENCE LATTICE OF AN EVENTUALLY REGULAR SEMIGROUP." International Journal of Algebra and Computation 06, no. 06 (1996): 655–85. http://dx.doi.org/10.1142/s0218196796000386.

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On any eventually regular semigroup S, congruences ν, μL, μR, μ, K, KL, KR, ζ are introduced which are the greatest congruences over: nil-extensions (n.e.) of completely simple semigroups, n.e. of left groups, n.e. of right groups, n.e. of groups, n.e. of rectangular bands, n.e. of left zero semigroups, n.e. of right zero semigroups, nil-semigroups, respectively. Each of these congruences is induced by a certain representation of S which is defined on an arbitrary semigroup. These congruences play an important role in the study of lattices of varieties, pseudovarieties and existence varieties.

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REN, XUEMING, DANDAN YANG, and K. P. SHUM. "ON LOCALLY EHRESMANN SEMIGROUPS." Journal of Algebra and Its Applications 10, no. 06 (2011): 1165–86. http://dx.doi.org/10.1142/s0219498811005129.

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It was first proved by McAlister in 1983 that every locally inverse semigroup is a locally isomorphic image of a regular Rees matrix semigroup over an inverse semigroup and Lawson in 2000 further generalized this result to some special locally adequate semigroups. In this paper, we show how these results can be extended to a class of locally Ehresmann semigroups.

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SALIOLA, FRANCO V. "THE QUIVER OF THE SEMIGROUP ALGEBRA OF A LEFT REGULAR BAND." International Journal of Algebra and Computation 17, no. 08 (2007): 1593–610. http://dx.doi.org/10.1142/s0218196707004219.

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Recently it has been noticed that many interesting combinatorial objects belong to a class of semigroups called left regular bands, and that random walks on these semigroups encode several well-known random walks. For example, the set of faces of a hyperplane arrangement is endowed with a left regular band structure. This paper studies the module structure of the semigroup algebra of an arbitrary left regular band, extending results for the semigroup algebra of the faces of a hyperplane arrangement. In particular, a description of the quiver of the semigroup algebra is given and the Cartan inv

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