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Covers for Monoids

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by John Fountain , Jean-Eric Pin , Pascal Weil
Citations:3 - 2 self
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BibTeX

@MISC{Fountain_coversfor,
    author = {John Fountain and Jean-Eric Pin and Pascal Weil},
    title = {Covers for Monoids},
    year = {}
}

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Abstract

In this contribution to the structure theory of semigroups, we propose a unified generalisation of a string of results on group extensions, originating on the one hand in the seminal structure and covering theorems of McAlister and on the other, in Ash's celebrated solution of the Rhodes conjecture in finite semigroup theory. McAlister proved that each inverse monoid admits an E-unitary cover, and gave a structure theorem for E-unitary inverse monoids. Subsequent generalisations extended one or both results to orthodox monoids (McAlister, Szendrei, Takizawa), regular monoids (Trotter), E-dense semigroups in which the idempotents form a semilattice (Margolis and Pin, Fountain), and E-dense semigroups in which the idempotents form a subsemigroup (Almeida, Pin and Weil, Zhonghao Jiang). We show that any E-dense monoid admits a D-unitary E-dense cover and we provide a structure theorem for D-unitary E-dense monoids, in terms of groups acting on a category. Here D(M) is the least weakly s...

Keyphrases

structure theorem    e-dense semigroups    e-dense monoid    e-unitary inverse monoids    subsequent generalisation    inverse monoid    e-unitary cover    group extension    zhonghao jiang    rhodes conjecture    d-unitary e-dense cover    regular monoids    orthodox monoids    unified generalisation    finite semigroup theory    d-unitary e-dense monoids    seminal structure    structure theory   

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