The Source of Semiprimeness of Semigroups

Abstract

In this study, we define new semigroup structures using the set S-S = {a is an element of S vertical bar aSa = 0} which is called the source of semiprimeness for a semigroup S with zero element. vertical bar S-S vertical bar-idempotent semigroup, vertical bar S-S vertical bar-regular semigroup, vertical bar S-S vertical bar-reduced semigroup, and vertical bar S-S vertical bar-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.