Green's relations and stability for subsemigroups
Group Theory
2019-07-11 v2 Rings and Algebras
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.
Cite
@article{arxiv.1906.02313,
title = {Green's relations and stability for subsemigroups},
author = {James East and Peter M. Higgins},
journal= {arXiv preprint arXiv:1906.02313},
year = {2019}
}
Comments
V2: 8 pages, referee suggestions incorporated, to appear in Semigroup Forum. V1: 6 pages