The Source of Semiprimeness of Semigroups

Abstract

In this study, we define new semigroup structures using the set SS=a∈S|aSa=0 which is called the source of semiprimeness for a semigroup S with zero element. SS−idempotent semigroup, SS−regular semigroup, SS−reduced semigroup, and SS−nonzero divisor semigroup which are generalizations of idempotent, regular, reduced, and nonzero divisor semigroups in semigroup theory are investigated, and their basic properties are determined. In addition, we adapt some well-known results in semigroup theory to these new semigroups.