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On left regular and intra-regular ordered semigroups
Mathematica Slovaca, 2014 We study the decomposition of left regular ordered semigroups into left regular components and the decomposition of intra-regular ordered semigroups into simple or intra-regular components, adding some additional information to the results considered in [
Niovi Kehayopulu, Michael Tsingelis
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Regular Orthocryptou Semigroups
Semigroup Forum, 2004The semigroups in this paper are defined using two kinds of generalized Green's relations defined elsewhere. A semigroup \(S\) is superabundant if each \(H^*\)-class contains an idempotent and \(S\) is semisuperabundant if both each \(\widetilde L\)- and \(\widetilde R\)-class contains at least one idempotent. A semigroup is a \(u\)-semigroup if it has
Wang, Zhengpan, Zhang, Ronghua, Xie, Mu
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Acta Mathematica Sinica, English Series, 2004
A semigroup \(S\) is called a weak regular *-semigroup if it has a unary operation * satisfying \[ xx^*x=x,\;(x^*)^*=x,\text{ and }(xx^*yy^*)^*=yy^*xx^*\text{ for all }x,y\text{ in }S. \] In this paper a type of partial algebra called a projective partial groupoid is defined.
Li, Yonghua, Kan, Haibin, Yu, Bingjun
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A semigroup \(S\) is called a weak regular *-semigroup if it has a unary operation * satisfying \[ xx^*x=x,\;(x^*)^*=x,\text{ and }(xx^*yy^*)^*=yy^*xx^*\text{ for all }x,y\text{ in }S. \] In this paper a type of partial algebra called a projective partial groupoid is defined.
Li, Yonghua, Kan, Haibin, Yu, Bingjun
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Applied Categorical Structures, 2003
Let \(\mathbf C\) be a category with vertex set \(V\) and arrow set \(A\). For \(a\in A\), \(a\sigma\in V\) is the source of \(a\) and \(a\tau\in V\) is the target of \(a\). A flow of \(\mathbf C\) is a mapping \(\varphi\colon V\to A\) such that \((x\varphi)\sigma=x\) for all \(x\in V\).
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Let \(\mathbf C\) be a category with vertex set \(V\) and arrow set \(A\). For \(a\in A\), \(a\sigma\in V\) is the source of \(a\) and \(a\tau\in V\) is the target of \(a\). A flow of \(\mathbf C\) is a mapping \(\varphi\colon V\to A\) such that \((x\varphi)\sigma=x\) for all \(x\in V\).
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Variants of Regular Semigroups
Semigroup Forum, 2001Let \(S\) be a semigroup and \(a\in S\); the semigroup with underlying set \(S\) and multiplication \(\circ\) defined by \(x\circ y=xay\) is a variant of \(S\), denoted \((S,a)\). An element of a regular semigroup is regularity preserving if \((S,a)\) is regular.
Khan, T. A., Lawson, M. V.
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Semigroup Forum, 1999
A regular \(*\)-semigroup is a semigroup \(S\) endowed with a supplementary operation \(*\) satisfying: (1) \(xx^*=x\), for every \(x\in S\); (2) \((x^*)^*=x\), for every \(x\in S\); (3) \((xy)^*=y^*x^*\), for every \(x,y\) in \(S\). It has been proved by \textit{M.
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A regular \(*\)-semigroup is a semigroup \(S\) endowed with a supplementary operation \(*\) satisfying: (1) \(xx^*=x\), for every \(x\in S\); (2) \((x^*)^*=x\), for every \(x\in S\); (3) \((xy)^*=y^*x^*\), for every \(x,y\) in \(S\). It has been proved by \textit{M.
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On Ordered Semigroups Which are Semilattices of Simple and Regular Semigroups
Communications in Algebra, 2013 We characterize the ordered semigroups which are decomposable into simple and regular components. We prove that each ordered semigroup which is both regular and intra-regular is decomposable into simple and regular semigroups, and the converse statement ...
Niovi Kehayopulu, Michael Tsingelis
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Left (Right) Regular Elements of Some Transformation Semigroups
Mathematics, 2023Ekkachai Laysirikul +1 more
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On Left Regular Ordered Semigroups
Southeast Asian Bulletin of Mathematics, 2002Niovi Kehayopulu +2 more
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