An Extended Class of Exponential Semigroups

In a series of articles during mid-eighties, Nagy has introduced the notion of WE-m-semigroups, generalizing exponential semigroups and assuming a left-right symmetry in the definition, which is not very much essential. The purpose of this paper is to obtain more general types of semigroups, termed 1 - WE-m/k and r-WE-m/k semigroups, which Include the earlier results of Nagy and are of a generic nature. For instance, any 1-WE-m/k semigroup is a semilattice of Archimedean semigroups of the same type.