Inverse semigroups with zero: Covers and their structure

Sydney Bulman-Fleming; John Fountain; Victoria Gould

Inverse semigroups with zero: Covers and their structure

Sydney Bulman-Fleming, John Fountain, Victoria Gould

Mathematics

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

Abstract

We obtain analogues, in the setting of semigroups with zero, of McAlister's covering theorem and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a class C of semigroups defined by modifying one of the many characterisations of E-unitary inverse semigroups, namely, that an inverse semigroup is E-unitary if and only if it is an inverse image of an idempotent-pure homomorphism onto a group. The class C is properly contained in the class of all E*-unitary inverse semigroups introduced by Szendrei but properly contains the class of strongly categorical Ef-unitary semigroups recently considered by Comes and Howie.

Original language	English
Pages (from-to)	15-30
Number of pages	16
Journal	Journal of the australian mathematical society series a-Pure mathematics and statistics
Volume	67
Publication status	Published - Aug 1999

Keywords

P-theorem
E*-unitary
cover
SEMILATTICES

Cite this

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title = "Inverse semigroups with zero: Covers and their structure",

abstract = "We obtain analogues, in the setting of semigroups with zero, of McAlister's covering theorem and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a class C of semigroups defined by modifying one of the many characterisations of E-unitary inverse semigroups, namely, that an inverse semigroup is E-unitary if and only if it is an inverse image of an idempotent-pure homomorphism onto a group. The class C is properly contained in the class of all E*-unitary inverse semigroups introduced by Szendrei but properly contains the class of strongly categorical Ef-unitary semigroups recently considered by Comes and Howie.",

keywords = "P-theorem, E*-unitary, cover, SEMILATTICES",

author = "Sydney Bulman-Fleming and John Fountain and Victoria Gould",

year = "1999",

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language = "English",

volume = "67",

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journal = "Journal of the australian mathematical society series a-Pure mathematics and statistics",

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publisher = "Australian Mathematical Society",

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TY - JOUR

T1 - Inverse semigroups with zero

T2 - Covers and their structure

AU - Bulman-Fleming, Sydney

AU - Fountain, John

AU - Gould, Victoria

PY - 1999/8

Y1 - 1999/8

N2 - We obtain analogues, in the setting of semigroups with zero, of McAlister's covering theorem and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a class C of semigroups defined by modifying one of the many characterisations of E-unitary inverse semigroups, namely, that an inverse semigroup is E-unitary if and only if it is an inverse image of an idempotent-pure homomorphism onto a group. The class C is properly contained in the class of all E*-unitary inverse semigroups introduced by Szendrei but properly contains the class of strongly categorical Ef-unitary semigroups recently considered by Comes and Howie.

AB - We obtain analogues, in the setting of semigroups with zero, of McAlister's covering theorem and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a class C of semigroups defined by modifying one of the many characterisations of E-unitary inverse semigroups, namely, that an inverse semigroup is E-unitary if and only if it is an inverse image of an idempotent-pure homomorphism onto a group. The class C is properly contained in the class of all E*-unitary inverse semigroups introduced by Szendrei but properly contains the class of strongly categorical Ef-unitary semigroups recently considered by Comes and Howie.

KW - P-theorem

KW - E-unitary

KW - cover

KW - SEMILATTICES

M3 - Article

SN - 0263-6115

VL - 67

SP - 15

EP - 30

JO - Journal of the australian mathematical society series a-Pure mathematics and statistics

JF - Journal of the australian mathematical society series a-Pure mathematics and statistics

ER -