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Green's relations and stability for subsemigroups

East, James and Higgins, Peter M (2019) 'Green's relations and stability for subsemigroups.' Semigroup Forum. ISSN 0037-1912

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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 sixty years, and which have sometimes been presented in different forms.

Item Type: Article
Uncontrolled Keywords: Green’s relations, Stability, Regularity, Subsemigroups
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 11 Jul 2019 11:47
Last Modified: 08 Aug 2019 11:15
URI: http://repository.essex.ac.uk/id/eprint/24968

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