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Green's relations and stability for subsemigroups

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arxiv 1906.02313 v2 pith:SLW3CU5Q submitted 2019-06-05 math.GR math.RA

James East , Peter M. Higgins This is my paper · ORCID
classification math.GRmath.RA
keywords greenstabilityrelationssemigroupssubsemigroupsappearedbeencarried
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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.

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Cited by 1 Pith paper

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  1. Idempotents and one-sided units: Lattice invariants and a semigroup of functors on the category of monoids

    math.GR 2019-08 accept novelty 6.0 of 10

    The lattice of submonoids generated by idempotents and one- or two-sided units of a monoid is classified by a four-bit type, and the functors producing these submonoids generate a 15-element monoid.

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