Associativity of the regular semidirect product of existence varieties
Bernd Billhardt, Mária B. Szendrei · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 2000
Abstract The associativity of the regular semidirect product of existence varieties introduced by Jones and Trotter was proved under certain condition by Reilly and Zhang. Here we estabilsh associativity in many new cases. Moreover, we prove that the regular semidirect product is right distributive with respect to the join operation. In particular, both associativity and right distriutivity yiel within the varieties of completely simple semigroups. Analogous results are obtainedj for e-pseudovarieties of finite regular semigroups.