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Congruences on *-Regular Semigroups
Periodica Mathematica Hungarica, 2002By a *-regular semigroup \(S\) the authors mean a semigroup with involution * admitting a Moore-Penrose inverse; that is, for each \(a\in S\) there exists a (necessarily unique) solution \(x\) to the equations \(axa=a\), \(xax=x\), \((ax)^*=ax\), \((xa)^*=xa\) which is denoted by \(x=a^+\).
Crvenković, Siniša, Dolinka, Igor
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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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Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1981
SynopsisA regular semigroup S is called V-regular if for any elements a, b ∈ S and any inverse (ab)′ of ab, there exists an inverse a′ of a and an inverse b′ of b such that (ab)′ = b′a′. A characterization of a V-regular semigroup is given in terms of its partial band of idempotents.
Nambooripad, K. S. S., Pastijn, F.
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SynopsisA regular semigroup S is called V-regular if for any elements a, b ∈ S and any inverse (ab)′ of ab, there exists an inverse a′ of a and an inverse b′ of b such that (ab)′ = b′a′. A characterization of a V-regular semigroup is given in terms of its partial band of idempotents.
Nambooripad, K. S. S., Pastijn, F.
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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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Perfect Completely Regular Semigroups
Mathematische Nachrichten, 1985A congruence \(\sigma\) on a semigroup \(S\) is called perfect if for all \(a,b\in S\) we have \((a\sigma)(b\sigma)=(ab)\sigma\) where \(a\sigma\) denotes the \(\sigma\)-class containing \(a\). If every congruence on \(S\) is perfect, \(S\) is called perfect. In this paper the author characterizes perfect completely regular semigroups.
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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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T-Classification of Regular Semigroups
Semigroup Forum, 2002The author proposes a scheme to classify regular semigroups and takes a first step in that direction. On the congruence lattice of any regular semigroup \(S\) are defined two relations, \(K\) and \(T\), the latter a congruence, the former only meet-preserving, in general.
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2021
This thesis was scanned from the print manuscript for digital preservation and is copyright the author. Researchers can access this thesis by asking their local university, institution or public library to make a request on their behalf. Monash staff and postgraduate students can use the link in the References field.
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This thesis was scanned from the print manuscript for digital preservation and is copyright the author. Researchers can access this thesis by asking their local university, institution or public library to make a request on their behalf. Monash staff and postgraduate students can use the link in the References field.
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Permutable regular \(\omega\)-semigroups
1988Let S be a semigroup. If every pair of congruences \(\rho\), \(\tau\) of S commutes, that is \(\rho \cdot \tau =\tau \cdot \rho\), then S is called a permutable semigroup. In this paper the authors study permutable regular \(\omega\)-semigroups i.e.
C. Bonzini, CHERUBINI, ALESSANDRA
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