SEMISIMPLE ELEMENTS IN HypG(2)

Abstract

In semigroup theory, it is of interest to consider various types of

semigroup elements, including regular, quasi-regular, completely quasi

regular, and semisimple elements. It is known that in general, regular

implies completely quasi-regular which in turn implies semisimple. In

this paper, we consider a particular semigroup, consisting of a type of

mappings called generalized hypersubstitutions. The main result of this

paper is that for this particular semigroup, any semisimple element is

also regular, making these conditions equivalent.