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Results 11 - 20
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92
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 conven-tional 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 a-regular. In this paper, we inves-tigated the least group congruence on an eventually conventional semi-group which alternating ..."
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to the least group congruence on E-inversive E-semigroup 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 0-E-unitary inverse semigroups of the P -representation of an E-unitary inverse semigroup. While we do not know if every 0-E-unitary 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 0-E-unitary inverse semigroups of the P -representation of an E-unitary inverse semigroup. While we do not know if every 0-E-unitary 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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-Schein-Nambooripad 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 (E-unitary) cover, and on the other
Some classes of factorizable semigroups∗
"... [Almost] factorizable inverse monoids [semigroups] play an impor-tant 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 impor-tant 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 E-unitary 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 Ehresmann-Schein-Nambooripad (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 Ehresmann-Schein-Nambooripad (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 poly-cylic monoids, and they arise in the study of Leavitt path algebras, Cohn path algebras, Cuntz-Krieger 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 poly-cylic monoids, and they arise in the study of Leavitt path algebras, Cohn path algebras, Cuntz-Krieger C∗-algebras, and Toeplitz C
PARTIAL ORDERS IN REGULAR SEMIGROUPS
, 2010
"... First we have obtained equivalent conditions for a regular semi-group and is equivalent to N = N1 It is observed that every regular semigroup is weakly separative and C ⊆ S and on a completely reg-ular 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 e-varieties, are obtained. For instance, as special cases of general results the e-variety 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
