Exponential permutable semigroups

Abstract

A semigroup  is called a permutable semigroup if  is satisfied for all congruences  and  of .  A semigroup is called an exponential semigroup if it satisfies the identity  for every integer . In this paper we deal with permutable exponential semigroups. We describe the archimedian exponential semigroups and non-archimedian exponential semigroups which are semilattices of a group and a nilpotent semigroup.