A characterization of adequate semigroups by forbidden subsemigroups
Group Theory
2017-06-23 v1
Abstract
A semigroup is \emph{amiable} if there is exactly one idempotent in each -class and in each -class. A semigroup is \emph{adequate} if it is amiable and if its idempotents commute. We characterize adequate semigroups by showing that they are precisely those amiable semigroups which do not contain isomorphic copies of two particular nonadequate semigroups as subsemigroups.
Cite
@article{arxiv.1111.4512,
title = {A characterization of adequate semigroups by forbidden subsemigroups},
author = {Joao Araujo and Michael Kinyon and Antonio Malheiro},
journal= {arXiv preprint arXiv:1111.4512},
year = {2017}
}