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Formations of orthodox semigroups
Semigroup Forum, 2023A semigroup \(S\) is said to be \textit{regular} if for each \(a\in S\) there is \(b\in S\) with \(aba = a\). An \textit{orthodox semigroup} is a regular semigroup whose set of idempotents is a subsemigroup. A class of orthodox semigroups is called a \textit{bivariety} if it is closed for orthodox subsemigroups, for quotients, and for direct products ...
Gomes, Gracinda M. S. +1 more
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Science in China Series A: Mathematics, 2009
Let \(S\) be a semigroup with the set of idempotents \(E(S)\). For \(a\in S\) and a non-empty subset \(U\subseteq E(S)\) denote \(U_a^r=\{u\in U\mid au=a\}\) and define relation \(\widetilde{\mathcal L}^U\) by \(a\widetilde{\mathcal L}^Ub\Leftrightarrow U_a^r=U_b^r \); definition of \(\widetilde{\mathcal R}^U\) is dual.
Ren, Xue-Ming +2 more
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Let \(S\) be a semigroup with the set of idempotents \(E(S)\). For \(a\in S\) and a non-empty subset \(U\subseteq E(S)\) denote \(U_a^r=\{u\in U\mid au=a\}\) and define relation \(\widetilde{\mathcal L}^U\) by \(a\widetilde{\mathcal L}^Ub\Leftrightarrow U_a^r=U_b^r \); definition of \(\widetilde{\mathcal R}^U\) is dual.
Ren, Xue-Ming +2 more
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Isbell’s Zigzag theorem for permutative orthodox semigroups and clifford semigroups
Asian-European Journal of Mathematics, 2021In this paper, we prove that the dominion of any full orthodox subsemigroup of a medial orthodox semigroup is described by the Isbell zigzag theorem in the category of medial orthodox semigroups. As a consequence, the dominions of any full completely regular subsemigroup of a medial completely regular semigroup as well as that of any full Clifford ...
Noor Alam, Noor Mohammad Khan
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ORTHODOX TRANSVERSALS OF REGULAR SEMIGROUPS
International Journal of Algebra and Computation, 2001Orthodox transversals were introduced by the first author as a generalization of inverse transversals [Comm. Algebra 27(9) (1999), pp. 4275–4288]. One of our aims in this note is to consider the general case of orthodox transversals. The main results are on the sets I and Λ, two components of regular semigroups with orthodox transversals.
Chen, J. F., Cuo, Y. Q.
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Weakly $$B$$ B -orthodox semigroups
Periodica Mathematica Hungarica, 2014In the introduction the author has written that ``the article [J. Algebra 368, 209-230 (2012; Zbl 1275.20067)] by \textit{V. Gould} and \textit{Y. Wang} is the first of three in which we investigate the correspondence between algebraic structures and ordered categories, in the sense of Ehresmann-Schein-Nambooripad\dots.
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Congruences on orthodox semigroups II
Journal of the Australian Mathematical Society, 1972If ρ is a congruence on a regular semigroup S, then the kernel of ρ is defined to be the set of ρ-classes which contain idempotents of S. Preston [7] has proved that two congruences on a regular semigroup coincide if and only if they have the same kernel: this naturally poses the problem of characterizing the kernel of a congruence on a regular ...
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STANDARD REPRESENTATIONS OF ORTHODOX SEMIGROUPS
Communications in Algebra, 2005Abstract Orthodox semigroups have been studied by many authors, in particular by Hall, Yamada and Petrich. In this paper, we give the standard representation of orthodox semigroups and investigate various e-varieties of orthodox semigroups which are determined by the standard representations.
Yong He, Yuqi Guo, K.P. Shum
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Almost Factorizable Orthodox Semigroups
Semigroup Forum, 2006In this paper, we investigate idempotent separating and arbitrary homomorphic images of semidirect products of bands by groups. We give characterizations for idempotent separating homomorphic images of semidirect products, and show that the class of all idempotent separating homomorphic images is strictly contained in the class of all homomorphic ...
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Semiprimitivity of Orthodox Semigroup Algebras
Communications in Algebra, 2016Let S be a finite orthodox semigroup or an orthodox semigroup where the idempotent band E(S) is locally pseudofinite. In this paper, by using principal factors and Rukolaǐne idempotents, we show that the contracted semigroup algebra R0[S] is semiprimitive if and only if S is an inverse semigroup and R[G] is semiprimitive for each maximal subgroup G of ...
Yingdan Ji, Yanfeng Luo
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On left quasinormal orthodox semigroups
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1983SynopsisThe existence of a smallest inverse congruence on an orthodox semigroup is known. It is also known that a regular semigroupSis locally inverse and orthodox if and only if there exists a local isomorphism fromSonto an inverse semigroupT.In this paper, we show the existence of a smallestR-unipotent congruence ρ on an orthodox semigroupSand give ...
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