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arXiv · 1111.4512

A characterization of adequate semigroups by forbidden subsemigroups

Joao Araujo·Michael Kinyon·Antonio Malheiro
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Abstract

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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Joao Araujo, Michael Kinyon, Antonio Malheiro. 2011-11-18. A characterization of adequate semigroups by forbidden subsemigroups. https://doi.org/10.1017/s030821051100182x

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