A characterization of adequate semigroups by forbidden subsemigroups

Details A characterization of adequate semigroups by forbidden subsemigroups A characterization of adequate semigroups by forbidden subsemigroups

2011-11-18

arxiv.org/abs/1111.4512v1

Mathematics

Group Theory

Scientific paper

A semigroup is \emph{amiable} if there is exactly one idempotent in each $\mathcal{R}^*$-class and in each $\mathcal{L}^*$-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.

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