\(p\)-regular semigroups (Q1281276)

\(P\)-regular semigroups were defined by M. Yamada and M. K. Sen in 1989. Omitting one axiom the authors introduce the new class of \(p\)-regular semigroups. Hence regular *-semigroups and orthodox semigroups are within the class of all \(p\)-regular semigroups. The main goal of the paper is to extend different results from \(P\)-regular semigroups to the theory of \(p\)-regular semigroups. In particular, the maximum idempotent separating congruence on a \(p\)-regular semigroup is described.