Finite proper covers in a class of finite semigroups with commuting idempotents

G.M.S. Gomes; V. Gould

doi:10.1007/s002330010144

Finite proper covers in a class of finite semigroups with commuting idempotents

G.M.S. Gomes, V. Gould

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Weakly left ample semigroups are a class of semigroups that are (2,1) -subalgebras of semigroups of partial transformations, where the unary operation takes a transformation a to the identity map in the domain of a . It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In this paper we show that for every finite weakly left ample semigroup S , there is a finite proper weakly left ample semigroup and an onto morphism from S to S which separates idempotents. In fact, S is actually a (2,1) -subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A).

Original language	English
Pages (from-to)	433-454
Number of pages	21
Journal	Semigroup Forum
Volume	66
Issue number	3
DOIs	https://doi.org/10.1007/s002330010144
Publication status	Published - Mar 2008

Keywords

Algebra

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10.1007/s002330010144

http://dx.doi.org/10.1007/s002330010144

Cite this

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title = "Finite proper covers in a class of finite semigroups with commuting idempotents",

abstract = "Weakly left ample semigroups are a class of semigroups that are (2,1) -subalgebras of semigroups of partial transformations, where the unary operation takes a transformation a to the identity map in the domain of a . It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In this paper we show that for every finite weakly left ample semigroup S , there is a finite proper weakly left ample semigroup and an onto morphism from S to S which separates idempotents. In fact, S is actually a (2,1) -subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A).",

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T1 - Finite proper covers in a class of finite semigroups with commuting idempotents

AU - Gomes, G.M.S.

AU - Gould, V.

PY - 2008/3

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N2 - Weakly left ample semigroups are a class of semigroups that are (2,1) -subalgebras of semigroups of partial transformations, where the unary operation takes a transformation a to the identity map in the domain of a . It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In this paper we show that for every finite weakly left ample semigroup S , there is a finite proper weakly left ample semigroup and an onto morphism from S to S which separates idempotents. In fact, S is actually a (2,1) -subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A).

AB - Weakly left ample semigroups are a class of semigroups that are (2,1) -subalgebras of semigroups of partial transformations, where the unary operation takes a transformation a to the identity map in the domain of a . It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In this paper we show that for every finite weakly left ample semigroup S , there is a finite proper weakly left ample semigroup and an onto morphism from S to S which separates idempotents. In fact, S is actually a (2,1) -subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A).

KW - Algebra

U2 - 10.1007/s002330010144

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M3 - Article

SN - 1432-2137

VL - 66

SP - 433

EP - 454

JO - Semigroup Forum

JF - Semigroup Forum

IS - 3

ER -