On commutative ideal semigroups. (Q1885186)

A semigroup \(S\) is called ideal if every congruence in \(S\) is a Rees congruence. A characterization of commutative ideal semigroups was obtained by \textit{K. D. Aucoin} [Semigroup Forum 50, No. 3, 295-300 (1995; Zbl 0831.20077)]. The authors find a gap in this result and correct the characterization considering two cases: \(S=ES\) and \(S\not=ES\), where \(E\) is the set of all idempotents. Some properties of commutative ideal semigroups are obtained.