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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, 2016 We give a complete description of the structure of all bisimple orthodox semigroups generated by two mutually inverse ...
A.H. Clifford +10 more
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Lattice isomorphisms of bisimple monogenic orthodox semigroups [PDF]
Semigroup Forum, 2011 Using the classification and description of the structure of bisimple monogenic orthodox semigroups obtained in \cite{key10}, we prove that every bisimple orthodox semigroup generated by a pair of mutually inverse elements of infinite order is strongly ...
A.H. Clifford +11 more
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End-completely-regular and end-inverse lexicographic products of graphs. [PDF]
ScientificWorldJournal, 2014 A graph X is said to be End‐completely‐regular (resp., End‐inverse) if its endomorphism monoid End(X) is completely regular (resp., inverse). In this paper, we will show that if X[Y] is End‐completely‐regular (resp., End‐inverse), then both X and Y are End‐completely‐regular (resp., End‐inverse).
Hou H, Gu R.
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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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Orthodox semigroups and permutation matchings [PDF]
Semigroup Forum, 2016 We determine when an orthodox semigroup S has a permutation that sends each member of S to one of its inverses and show that if such a permutation exists, it may be taken to be an involution. In the case of a finite orthodox semigroup the condition is an effective one involving Green's relations on the combinatorial images of the principal factors of S.
P. Higgins
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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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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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Certain congruences on orthodox semigroups [PDF]
Pacific Journal of Mathematics, 1976 Let \(S\) be a regular semigroup and \(E\) be the set of all its idempotents. The semigroup \(S\) is called unitary semigroup if \(e,ea\in E\) implies \(a\in E\) for all \(a,e\in S\). Regular semigroups are described which are underdirect products of unitary semigroups and semilattices of groups.
J. Mills
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Congruences on orthodox semigroups [PDF]
Bulletin of the Australian Mathematical Society, 1970 J. C. Mealcin
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