Further results in the theory of generalised inflations of semigroups. (Q927290)

A broad version of generalized inflation of semigroups given by \textit{G. T. Clarke} and \textit{R. A. R. Monzo} [Semigroup Forum 60, No. 2, 172-186 (2000; Zbl 0951.20045)] is defined. The semigroups satisfying the condition \(xyzw\in\{xy,xw,zy,zw\}\) are precisely those whose power semigroup is a generalized inflation of a band. The structure of generalized inflations is determined for the following types of semigroups: the direct product of a group and a band, a completely simple semigroup and a free semigroup \(F(X)\) on a set \(X\). In some cases a generalized inflation coincides with an inflation.