Results 181 to 190 of about 1,070,702 (215)
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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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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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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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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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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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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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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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