Some idempotent-separating congruences on a 𝜋-regular semigroups

Abstract

Edwards describes in [4] the maximum idempotent-separating congruence on a eventually regular (equivalently, 𝜋 -regular) semigroup which is given by(Error rendering LaTeX formula). In this paper we describe the maximum idempotent-separating congruence and their kernels on some subclasses of 𝜋-regular semigroups. Also, we describe the minimum idempotent-separating r- semiprime congruence and its kernel on an r-semigroup.In this way we obtain a generalization of results of Meakin [10],[11], Feigenbaum [5],[6]and Howie[8].