Eventually regular Dubreil-Jacotin semigroups

T S  Blyth; G A  Pinto

doi:10.1007/s00233-004-0136-y

Eventually regular Dubreil-Jacotin semigroups

T S Blyth, G A Pinto

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

Abstract

We derive necessary and sufficient conditions for an ordered eventually regular semigroup to be a Dubreil-Jacotin semigroup. We show that an eventually regular Dubreil-Jacotin semigroup has a biggest idempotent. Necessary and sufficient conditions for this biggest idempotent to be a weak middle unit or to be medial are related to the semigroup being naturally ordered and to the set of regular elements being a subsemigroup.

Original language	English
Pages (from-to)	431-440
Number of pages	10
Journal	Semigroup Forum
Volume	69
DOIs	https://doi.org/10.1007/s00233-004-0136-y
Publication status	Published - Nov 2004

Keywords

eventually regular semigroup
Dubreil-Jacotin semigroup
weak middle unit
medial idempotent

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10.1007/s00233-004-0136-y

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title = "Eventually regular Dubreil-Jacotin semigroups",

abstract = "We derive necessary and sufficient conditions for an ordered eventually regular semigroup to be a Dubreil-Jacotin semigroup. We show that an eventually regular Dubreil-Jacotin semigroup has a biggest idempotent. Necessary and sufficient conditions for this biggest idempotent to be a weak middle unit or to be medial are related to the semigroup being naturally ordered and to the set of regular elements being a subsemigroup.",

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AU - Pinto, G A

PY - 2004/11

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N2 - We derive necessary and sufficient conditions for an ordered eventually regular semigroup to be a Dubreil-Jacotin semigroup. We show that an eventually regular Dubreil-Jacotin semigroup has a biggest idempotent. Necessary and sufficient conditions for this biggest idempotent to be a weak middle unit or to be medial are related to the semigroup being naturally ordered and to the set of regular elements being a subsemigroup.

AB - We derive necessary and sufficient conditions for an ordered eventually regular semigroup to be a Dubreil-Jacotin semigroup. We show that an eventually regular Dubreil-Jacotin semigroup has a biggest idempotent. Necessary and sufficient conditions for this biggest idempotent to be a weak middle unit or to be medial are related to the semigroup being naturally ordered and to the set of regular elements being a subsemigroup.

KW - eventually regular semigroup

KW - Dubreil-Jacotin semigroup

KW - weak middle unit

KW - medial idempotent

U2 - 10.1007/s00233-004-0136-y

DO - 10.1007/s00233-004-0136-y

M3 - Article

SN - 1432-2137

VL - 69

SP - 431

EP - 440

JO - Semigroup Forum

JF - Semigroup Forum

ER -

Eventually regular Dubreil-Jacotin semigroups

Abstract

Keywords

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