A class of quasi-adequate semigroups. (Q2460687)

An abundant semigroup \(S\) is said to be quasi-adequate if its idempotents form a subsemigroup of \(S\). Quasi-adequate semigroups have been studied by \textit{A. El-Qallali} and \textit{J. B. Fountain} [Proc. R. Soc. Edinb., Sect. A 91, 91-99 (1981; Zbl 0501.20042)] using an equivalence relation \(\delta\). In the present paper the authors construct a class of semigroups called \(QT\)-systems, and show that each \(QT\)-system is a quasi-adequate semigroup on which \(\delta\) is a congruence. ``Conversely'', they prove that each quasi-adequate semigroup on which \(\delta\) is a congruence is isomorphic to a \(QT\)-system.