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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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A class of regular semigroups with regular *- transversals
Semigroup Forum, 2002A regular semigroup \(S\) is called a regular \(*\)-semigroup if there is a unary operation \(*\) which satisfies the following three conditions: (i) \(xx^*x=x\), (ii) \((x^*)^*=x\), and (iii) \((xy)^*=y^*x^*\), for any \(x,y\in S\) [\textit{T. E. Nordahl, H. E. Scheiblich}, Semigroup Forum 16, 369-377 (1978; Zbl 0408.20043)]. If there a subsemigroup \(
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The lattice of regular subsemigroups of a regular semigroup
Vestnik St. Petersburg University: Mathematics, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Characterization of *-Congruences on a Regular *-Semigroup
Semigroup Forum, 1998A semigroup \(S\) with a unary operation \(*\colon S\to S\) satisfying the identities \((x^*)^*=x\) and \((xy)^*=y^*x^*\) is called a *-semigroup. A *-semigroup \(S\) is a regular *-semigroup if also the identity \(x=xx^*x\) holds on \(S\). The symbol \(\Lambda^*(S)\) denotes the lattice of all *-congruences on a regular *-semigroup \(S\).
Chae, Younki +2 more
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REGULAR SEMIGROUPS WITH INVERSE TRANSVERSALS
The Quarterly Journal of Mathematics, 1983An inverse subsemigroup T of a regular semigroup S is said to be an inverse transversal of S if T contains precisely one inverse of each element of S. Constructions based on the regular semigroup consisting of all regular elements of a Rees matrix semigroup over an inverse semigroup are used to establish the paper's main results.
McAlister, D. B., McFadden, R. B.
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Stability of C-regularized Semigroups
Acta Mathematica Sinica, English Series, 2004Let \(X\) be a Banach space, let \(T=\{T(t)\}_{t \geq 0}\) be a bounded \(C\)-regularized semigroup generated by \(A\), where \(C\) is a bounded injective linear operator on \(X\) such that \(R(C)\) is dense in \(X\). Denoting by \(\sigma_u(A, Cx)\) the set of all points \(\lambda \in i {\mathbb R}\) such that \((\lambda - A)^{-1}Cx\) cannot be ...
Li, Miao, Zheng, Quan
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Orders in completely regular semigroups
Mathematika, 2001A classic theorem of semigroup theory is that a semigroup \(S\) has a group of quotients if and only if it is reversible and cancellative. From the perspective of the group, it contains \(S\) as an ``order''. Generalizing from both this situation and from ring theory, a semigroup \(S\) is an order in another semigroup \(Q\) if every element in \(Q ...
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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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Semilattices of simple and regular n-ary semigroups
Semigroup Forum, 2023Jukkrit Daengsaen +1 more
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On Right Weakly Regular Semigroups of Generalized Bipolar Fuzzy Subsemigroups
Missouri Journal of Mathematical Sciences, 2021Pannawit Khamrot
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