Maximal orders in completely 0-simple semigroups (Q1857392)

This article continues the work of the paper by the same authors and \textit{P. Smith} [Commun. Algebra 27, No. 1, 173-187 (1999; Zbl 0922.20064)] on maximal orders in semigroups. The emphasis is on orders in completely \(0\)-simple semigroups. In such semigroups \(Q\), orders \(S\) are related to the semigroup \({\mathcal F}(S)\) of all fractional \(S\)-ideals of \(Q\). More specific results are obtained in the case \(S\) is abundant or \(Q\) is a Brandt semigroup.