Journal ArticleDOI
Embedding Into Almost Left Factorizable Restriction Semigroups
TLDR
In this paper, the authors adapted the notion of almost left factorizability to restriction semigroups and proved that each restriction semigroup is embeddable into an almost left-factorizable restriction semgroup.Abstract:
The notion of almost left factorizability and the results on almost left factorizable weakly ample semigroups, due to Gomes and the author, are adapted for restriction semigroups. The main result of the paper is that each restriction semigroup is embeddable into an almost left factorizable restriction semigroup. This generalizes a fundamental result of the structure theory of inverse semigroups.read more
Citations
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Partial monoid actions and a class of restriction semigroups
TL;DR: In this paper, the authors study classes of proper restriction semigroups determined by properties of partial actions underlying them, such as strongness, antistrongness, being defined by a homomorphism, being an action etc.
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Almost perfect restriction semigroups
TL;DR: In this paper, it was shown that every restriction semigroup is isomorphic to a W-product W (T, Y ), where T is a monoid, Y is a semilattice and there is a homomorphism from T into the inverse semigroup TI Y of isomorphisms between ideals of Y.
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Partial monoid actions and a class of restriction semigroups
TL;DR: In this article, the authors study classes of proper restriction semigroups determined by properties of partial actions underlying them, such as strongness, antistrongness, being defined by a homomorphism, being an action etc.
Journal ArticleDOI
Embedding in factorisable restriction monoids
TL;DR: In this paper, it was shown that each restriction semigroup has a proper cover which is embeddable in a semidirect product of a semilattice by a group.
Journal ArticleDOI
Two-sided expansions of monoids
TL;DR: In this paper, the study of expansions of monoids in the class of two-sided restriction monoids was initiated, and it was shown that generalizations of the Birget-Rhodes prefix group expansion, despite the absence of involu...
References
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Book
Inverse Semigroups, the Theory of Partial Symmetries
TL;DR: Inverse semigroups as mentioned in this paper, Ehresmann's maximum enlargement theorem complements the type II theorem of inverse monoids and formal languages for inverse monoid inverse semiggroups.
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Groups, semilattices and inverse semigroups. II
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E-unitary covers for inverse semigroups
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The free ample monoid
TL;DR: It is shown that the free weakly E-ample monoid on a set X is a full submonoid of the free inverse monoid FIM(X) on X, and so coincides with both thefree weakly ample and the free ample monoid FAM(X).