Idempotent-equivalent congruences on orthodox semigroups

Abstract

Any congruence on a semigroup S with a nonempty set E_s of idempotents induces a partition of the set E_s. Two congruences ρ and σ on the semigroup S are defined to be idempotent-equivalent congruences on S if ρ and σ induce the same partition of E_s. In this paper we investigate idempotent-equivalent congruences on orthodox semigroups (regular semigroups in which the set of idempotents forms a subsemigroup).