On a wreath product embedding for regular semigroups
The problem of wreath product embeddings in the theory of inverse semigroups has been studied in previous papers of the author [Semigroup Forum 44, 320-331 and 364-372 (1992; Zbl 0747.20032 and Zbl 0758.20019)]. On the other hand, \textit{M. B. Szendrei} [ibid. 32, 87-96 (1985; Zbl 0564.20037); and Proc. R. Soc. Edinb., Sect. A 106, 89-102 (1987; Zbl 0628.20052)] proved that every \(E\)-unitary regular semigroup with regular band of idempotents \(E\) can be embedded in a semidirect product of a band \(B\) by a group, where \(B\) belongs to the variety of bands generated by \(E\). In this paper, for a regular semigroup \(S\) a wreath product embedding is given, which depends on a group congruence on \(S\), satisfying a certain condition. As applications, wreath product embeddings for certain \(E\)- unitary regular semigroups are considered, and a short alternative proof of Szendrei's result above is established.
scientific article; zbMATH DE number 150432
scientific article