Results 221 to 230 of about 1,010,344 (260)
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Fuzzy congruences on a regular semigroup
Fuzzy Sets and Systems, 2001The paper examines lattices of fuzzy equivalence relations [cf. \textit{L. A. Zadeh}, Inf. Sci. 3, 177-200 (1971; Zbl 0218.02058)] on a regular semigroup. In particular properties of the lattice of fuzzy congruences are considered. This is a continuation of a paper by \textit{M. A. Samhan} [Inf. Sci. 74, No. 1-2, 165-175 (1993; Zbl 0785.20034)].
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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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Inverse semigroup congruencel on regular semigroups
Acta Mathematica Hungarica, 1969exaly +2 more sources
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 f -derivations, regular f -derivations and semigroup of f -derivations on PMS-algebras [PDF]
Berhanu Assaye Alaba
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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.
J. F. Chen, Y. Q. Cuo
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