SEMISIMPLE ELEMENTS IN HypG(2)
In semigroup theory, it is of interest to consider various types of semigroup elements, including regular, quasi-regular, completely quasiregular, 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.