Green's relations and stability for subsemigroups

James East; Peter M. Higgins

doi:10.1007/s00233-019-10039-8

Green's relations and stability for subsemigroups

James East, Peter M. Higgins

Western Sydney University

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

Abstract

We prove new results on inheritance of Green’s relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular that not all right-stable semigroups are embeddable in left-stable semigroups. This is carried out in the context of a survey of the various closely related notions of stability and minimality of Green’s classes that have appeared in the literature over the last 60 years, and which have sometimes been presented in different forms.

Original language	English
Pages (from-to)	77-86
Number of pages	10
Journal	Semigroup Forum
Volume	101
Issue number	1
DOIs	https://doi.org/10.1007/s00233-019-10039-8
Publication status	Published - 2020

Keywords

semigroup algebras
semigroups
stability

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10.1007/s00233-019-10039-8

Cite this

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title = "Green's relations and stability for subsemigroups",

abstract = "We prove new results on inheritance of Green{\textquoteright}s relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular that not all right-stable semigroups are embeddable in left-stable semigroups. This is carried out in the context of a survey of the various closely related notions of stability and minimality of Green{\textquoteright}s classes that have appeared in the literature over the last 60 years, and which have sometimes been presented in different forms.",

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AB - We prove new results on inheritance of Green’s relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular that not all right-stable semigroups are embeddable in left-stable semigroups. This is carried out in the context of a survey of the various closely related notions of stability and minimality of Green’s classes that have appeared in the literature over the last 60 years, and which have sometimes been presented in different forms.

KW - semigroup algebras

KW - semigroups

KW - stability

UR - http://hdl.handle.net/1959.7/uws:52751

U2 - 10.1007/s00233-019-10039-8

DO - 10.1007/s00233-019-10039-8

M3 - Article

SN - 0037-1912

VL - 101

SP - 77

EP - 86

JO - Semigroup Forum

JF - Semigroup Forum

IS - 1

ER -

Green's relations and stability for subsemigroups

Abstract

Keywords

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