Semigroups with zero whose idempotents form a subsemigroup

GMS Gomes; John Mackintosh Howie

doi:10.1017/S0308210500012786

Semigroups with zero whose idempotents form a subsemigroup

GMS Gomes, John Mackintosh Howie

Applied Mathematics

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

Abstract

The structure of a categorical, E*-dense, E*-unitary E-semigroup S is elucidated in terms of a 'B-quiver', where B is a primitive inverse semigroup. In the case where S is strongly categorical, B is a Brandt semigroup. A covering theorem is also proved, to the effect that every categorical E*-dense E-semigroup has a cover which is a categorical, E*-dense, E*-unitary E-semigroup.

Original language	English
Pages (from-to)	265-281
Number of pages	17
Journal	Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
Volume	128
Issue number	2
DOIs	https://doi.org/10.1017/S0308210500012786
Publication status	Published - Jan 1998

Keywords

INVERSE-SEMIGROUPS
SEMILATTICES
CONGRUENCES

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10.1017/S0308210500012786

Cite this

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abstract = "The structure of a categorical, E*-dense, E*-unitary E-semigroup S is elucidated in terms of a 'B-quiver', where B is a primitive inverse semigroup. In the case where S is strongly categorical, B is a Brandt semigroup. A covering theorem is also proved, to the effect that every categorical E*-dense E-semigroup has a cover which is a categorical, E*-dense, E*-unitary E-semigroup.",

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AU - Howie, John Mackintosh

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AB - The structure of a categorical, E*-dense, E*-unitary E-semigroup S is elucidated in terms of a 'B-quiver', where B is a primitive inverse semigroup. In the case where S is strongly categorical, B is a Brandt semigroup. A covering theorem is also proved, to the effect that every categorical E*-dense E-semigroup has a cover which is a categorical, E*-dense, E*-unitary E-semigroup.

KW - INVERSE-SEMIGROUPS

KW - SEMILATTICES

KW - CONGRUENCES

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DO - 10.1017/S0308210500012786

M3 - Article

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VL - 128

SP - 265

EP - 281

JO - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

IS - 2

ER -

Semigroups with zero whose idempotents form a subsemigroup

Abstract

Keywords

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