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Presentations of semigroups and embeddings in inverse semigroups
"... Let $X $ be a finite set of alphabets, $X^{*} $ the free monoid generated by $X $ and $R $ a finite set of $X^{*}\cross X^{*} $. Then let (X; $R$) denote the factor semigroup of $X^{*} $ modulo the congruence generated by the relation $R $. Then we say that a semigroup $S $ has a representation (X; ..."
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; $R$) if $S $ is isomorphic to (X; $R$). In this paper, we study relation $R $ for which $S=(X;R) $ can be embedded in an inverse semigroup. Stephen [2] gave a method of studying word problems for inverse semigroups with a presentation in terms of inverse word graphs. We shall apply this method
The Least Group Congruence on Conventional Regular Semigroups
"... An eventually regular semigroup S is said to be eventually conventional if aE(S)an−1(an) ′ ⊆ E(S) and an−1(an)′E(S)a ⊆ E(S) for each a ∈ S, (an) ′ ∈ W (an) where an is aregular. In this paper, we investigated the least group congruence on an eventually conventional semigroup which alternating ..."
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to the least group congruence on Einversive Esemigroup considered by Weipoltshammer [5]. Mathematics Subject Classification: 20M10
Geometric Representations of Inverse Semigroups
, 2000
"... This paper introduces the notion of a geometric representation of an inverse semigroup, a generalization to 0Eunitary inverse semigroups of the P representation of an Eunitary inverse semigroup. While we do not know if every 0Eunitary inverse semigroup has such a representation, many impor ..."
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This paper introduces the notion of a geometric representation of an inverse semigroup, a generalization to 0Eunitary inverse semigroups of the P representation of an Eunitary inverse semigroup. While we do not know if every 0Eunitary inverse semigroup has such a representation, many
RESTRICTION AND EHRESMANN SEMIGROUPS
 PROCEEDING OF ICA 2010
, 2010
"... Inverse semigroups form a variety of unary semigroups, that is, semigroups equipped with an additional unary operation, in this case a ↦ → a−1. The theory of inverse semigroups is perhaps the best developed within semigroup theory, and relies on two factors: an inverse semigroup S is regular, and ..."
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Cited by 4 (0 self)
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ScheinNambooripad characterisation of inverse semigroups in terms of inductive groupoids, (b) Munn’s use of fundamental inverse semigroups and his construction of the semigroup TE from a semilattice E, and (c) McAlister’s results showing on the one hand that every inverse semigroup has a proper (Eunitary) cover, and on the other
Some classes of factorizable semigroups∗
"... [Almost] factorizable inverse monoids [semigroups] play an important rule in the theory of inverse semigroups (see for example [2]). The notion of “factorizable ” and “almost factorizable ” coincides for inverse monoids. A couple of crucial results for inverse semigroups S are the following: a) S i ..."
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[Almost] factorizable inverse monoids [semigroups] play an important rule in the theory of inverse semigroups (see for example [2]). The notion of “factorizable ” and “almost factorizable ” coincides for inverse monoids. A couple of crucial results for inverse semigroups S are the following: a
Partial actions of groups their globalisations and Eunitary inverse semigroups
, 1999
"... A group G is said to act partially on a set Y if there is a map : G ! I(Y ) into the semigroup of partial bijections on X such that (g)(h) (gh) and (g) = (g ) for all g; h 2 G. We prove that each partial group action is the restriction of a universal global group action, and show that thi ..."
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Cited by 2 (0 self)
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A group G is said to act partially on a set Y if there is a map : G ! I(Y ) into the semigroup of partial bijections on X such that (g)(h) (gh) and (g) = (g ) for all g; h 2 G. We prove that each partial group action is the restriction of a universal global group action, and show
RESTRICTION SEMIGROUPS AND INDUCTIVE CONSTELLATIONS
, 2009
"... The EhresmannScheinNambooripad (ESN) Theorem, stating that the category of inverse semigroups and morphisms is isomorphic to the category of inductive groupoids and inductive functors, is a powerful tool in the study of inverse semigroups. Armstrong and Lawson have successively extended the ESN T ..."
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Cited by 6 (3 self)
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The EhresmannScheinNambooripad (ESN) Theorem, stating that the category of inverse semigroups and morphisms is isomorphic to the category of inductive groupoids and inductive functors, is a powerful tool in the study of inverse semigroups. Armstrong and Lawson have successively extended the ESN
Topological Graph Inverse Semigroups
, 2014
"... To every directed graph E one can associate a graph inverse semigroup G(E), where elements roughly correspond to possible paths in E. These semigroups generalize polycylic monoids, and they arise in the study of Leavitt path algebras, Cohn path algebras, CuntzKrieger C∗algebras, and Toeplitz C∗a ..."
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To every directed graph E one can associate a graph inverse semigroup G(E), where elements roughly correspond to possible paths in E. These semigroups generalize polycylic monoids, and they arise in the study of Leavitt path algebras, Cohn path algebras, CuntzKrieger C∗algebras, and Toeplitz C
PARTIAL ORDERS IN REGULAR SEMIGROUPS
, 2010
"... First we have obtained equivalent conditions for a regular semigroup and is equivalent to N = N1 It is observed that every regular semigroup is weakly separative and C ⊆ S and on a completely regular semigroup S ⊆ N and S is partial order. It is also obtained that a band (S,.) is normal iff C = N. ..."
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. It is also observed that on a completely regular semigroup (S,.), C = S = N iff (S,.) is locally inverse semigroup and the restriction of C to E(S) is the usual partial order on E(S). Finally it is obtained that, if (S,.) is a normal band of groups then C = S = N. Key Words: Locally inverse semigroup
Semidirect Products of Regular Semigroups
 Trans. Amer. Math. Soc
, 1999
"... Within the usual semidirect product S T of regular semigroups S and T lies the set Reg (S T ) of its regular elements. Whenever S or T is completely simple, Reg (S T ) is a (regular) subsemigroup. It is this `product' that is the theme of the paper. It is best studied within the framework ..."
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Cited by 4 (4 self)
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of this product, together with decompositions of many important evarieties, are obtained. For instance, as special cases of general results the evariety LI of locally inverse semigroups is decomposed as I RZ, where I is the variety of inverse semigroups and RZ is that of right zero semigroups; and the e
Results 11  20
of
92