A semigroup is amiable if there is exactly one idempotent in each ℛ*-class and in each ℒ*-class. A semigroup is adequate if it is amiable and if its idempotents commute. We characterize adequate semigroups by showing that they are precisely those amiable semigroups that do not contain isomorphic copies of two particular non-adequate semigroups as subsemigroups.
|Journal||Proceedings Of The Royal Society Of Edinburgh Section A-Mathematics|
|Publication status||Published - 1 Jan 2013|