Results 201 to 210 of about 1,595,421 (249)
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The commuting inverse along an element in semigroups
Communications in Algebra, 2021In this article, we consider commuting properties of the generalized inverse along one element and two elements. The conditions for the existence of the solution to the equation under the Green’s relation are given.
Long Wang, D. Mosić, H. Yao
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Semigroups of inverse quotients
Periodica Mathematica Hungarica, 2012The paper discusses the notion of left I-quotients in inverse semigroups. A subsemigroup \(S\) of an inverse semigroup \(Q\) is called a left I-order in \(Q\) (and \(Q\) is a semigroup of left I-quotients of \(S\)) if every \(q\in Q\) can be written as \(q=a^{-1}b\) where \(a,b\in S\).
Nassraddin Ghroda, Victoria Gould
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On Finite Semigroups Embeddable in Inverse Semigroups
Semigroup Forum, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mathematical Proceedings of the Cambridge Philosophical Society, 1961
Drazin (2) has recently introduced the concept of a pseudo-invertible element of an associative ring or semigroup. In this note we first show that such an element of a semigroup S may be characterized by the fact that some power of it lies in a subgroup of S.
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Drazin (2) has recently introduced the concept of a pseudo-invertible element of an associative ring or semigroup. In this note we first show that such an element of a semigroup S may be characterized by the fact that some power of it lies in a subgroup of S.
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EMBEDDING INVERSE SEMIGROUPS IN BISIMPLE CONGRUENCE-FREE INVERSE SEMIGROUPS
The Quarterly Journal of Mathematics, 1983The authors prove that for every infinite cardinal m there exists a bisimple congruence-free inverse semigroup \(S_ m\) with \(| S_ m| =2^ m\) such that every inverse semigroup of cardinal not exceeding m can be embedded in \(S_ m\). They also show that if S is an inverse semigroup and if \(m=| S|\) if \(| S|\) is infinite and \(m=\aleph_ 0\) otherwise,
Leemans, H., Pastijn, F.
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SemiGroup Forum, 2000
For a given set \(X\), denote by \(G_X\) the set of finite directed trees whose edges are labelled by members of \(X\), with two distinguished vertices. In this note, using techniques of rewriting theory, a new proof is given of the theorem of Munn that the free inverse semigroup on \(X\) is isomorphic to a semigroup defined on the set of so-called ...
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For a given set \(X\), denote by \(G_X\) the set of finite directed trees whose edges are labelled by members of \(X\), with two distinguished vertices. In this note, using techniques of rewriting theory, a new proof is given of the theorem of Munn that the free inverse semigroup on \(X\) is isomorphic to a semigroup defined on the set of so-called ...
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REPRESENTATIONS OF LOCALLY INVERSE *-SEMIGROUPS
International Journal of Algebra and Computation, 1996The first author obtained a generalization of Preston-Vagner Representation Theorem for generalized inverse *-semigroups. In this paper, we shall generalize their results for locally inverse *-semigroups. Firstly, by introducing a concept of a π-set (which is slightly different from the one in [7]), we shall construct the π-symmetric locally inverse *
Teruo Imaoka +2 more
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THE HOMOTOPY THEORY OF INVERSE SEMIGROUPS
International Journal of Algebra and Computation, 2002We show that abstract homotopy theory can be used to define a suitable notion of homotopy equivalence for inverse semigroups. As an application of our theory, we prove a theorem for inverse semigroup homomorphisms which is the exact counterpart of the well-known result in topology which states that every continuous function can be factorized into a ...
Mark V. Lawson +2 more
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On a Class of Inverse Semigroups
American Journal of Mathematics, 1962In this note we investigate the structure of a special class of inverse sernigroups-inverse semigroups the non-zero idempotents of which are primitive. We show that an inverse semigroup S has its non-zero idempoteits primitive if and only if it is a class sum of its Brandt ideals. A set of other equivalent conditions on S is also obtained.
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On equations in inverse semigroups
Algebra Universalis, 2002It is shown for an inverse semigroup \(\mathcal S\) which is not a group, the system \(x_1=x_2\) and \(x_3=x_4\) of equations in \(\mathcal S\) is not equivalent to any equation as well as the disjunction \(x_1=x_2\) or \(x_3=x_4\).
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