Results 1 to 10 of about 541 (105)
International Journal of Mathematics and Mathematical Sciences, 1990 Let M={a,b,c,…} and Γ={α,β,γ,…} be two non-empty sets. M is called a Γ-semigroup if aαb∈M, for α∈Γ and b∈M and (aαb)βc=aα(bβc), for all a,b,c∈M and for all α,β∈Γ. A semigroup can be considered as a Γ-semigroup.
M. K. Sen, N. K. Saha
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Bisimple monogenic orthodox semigroups [PDF]
Semigroup Forum, 2008 We give a complete description of the structure of all bisimple orthodox semigroups generated by two mutually inverse elements.
A.H. Clifford +10 more
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International Journal of Mathematics and Mathematical Sciences, 2011 It has been well known that the band of idempotents of a naturally ordered orthodox semigroup satisfying the “strong Dubreil-Jacotin condition” forms a normal band.
Shouxu Du, Xinzhai Xu, K. P. Shum
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The Relationship between E‐Semigroups and R‐Semigroups
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 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.
Ze Gu, Xuanlong Ma
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Unit orthodox semigroups [PDF]
Glasgow Mathematical Journal, 1983 Let S be a regular semigroup. Given x ∈ S, we shall say that a ∈ S is an associate of x if xax = x. The set of associates of x ∈ S will be denoted by A(x). Now suppose that S has an identity element 1. Let H1 denote the group of units of S. Then we say that u ∈ S is a unit associate of x whenever u ∈ A(x)∩Hl. In what follows we shall write U(x) = A(x)∩=
Blyth, T. S., McFadden, R.
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Some results on semigroups of transformations with restricted range
Open Mathematics, 2021 Let XX be a non-empty set and YY a non-empty subset of XX. Denote the full transformation semigroup on XX by T(X)T\left(X) and write f(X)={f(x)∣x∈X}f\left(X)=\{f\left(x)| x\in X\} for each f∈T(X)f\in T\left(X). It is well known that T(X,Y)={f∈T(X)∣f(X)⊆Y}
Yan Qingfu, Wang Shoufeng
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HOMOGENEOUS COMPLETELY SIMPLE SEMIGROUPS
Mathematika, Volume 66, Issue 3, Page 733-751, July 2020., 2020 Abstract A semigroup is completely simple if it has no proper ideals and contains a primitive idempotent. We say that a completely simple semigroup S is a homogeneous completely simple semigroup if any isomorphism between finitely generated completely simple sub‐semigroups of S extends to an automorphism of S.
Thomas Quinn‐Gregson
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Journal of Algebra, 2012 Let \(S\) be a semigroup and \(\emptyset\neq B\subseteq E(S)\). Let \(\widetilde{\mathcal L}_B\) be an equivalence relation, so that for \(a,b\in S\), \(a\widetilde{\mathcal L}_Bb\) if and only if \(\{e\in B:ae=a\}=\{e\in B:be=b\}\). A semigroup \(S\) is said to be \textit{weakly B-abundant} if every \(\widetilde{\mathcal L}_B\)-class and every ...
Gould, Victoria, Wang, Yanhui
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Open Mathematics, 2015 In this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely Vn-semigroups, is introduced.
Gu Ze, Tang Xilin
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Idempotent 2x2 matrices over linearly ordered abelian groups [PDF]
Categories and General Algebraic Structures with ApplicationsIn this paper we study multiplicative semigroups of $2\times 2$ matrices over a linearly ordered abelian group with an externally added bottom element. The multiplication of such a semigroup is defined by replacing addition and multiplication by join and
Valdis Laan, Marilyn Kutti
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