The source of semiprimeness of semigroups (Q2230036)

Summary: In this study, we define new semigroup structures using the set \(S_S=\{a \in S \mid a S a = 0\}\) which is called the source of semiprimeness for a semigroup \(S\) with zero element. \(|S_S|\)-idempotent semigroup, \(|S_S|\)-regular semigroup, \(|S_S|\)-reduced semigroup, and \(| S_S|\)-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.