The Source of Semiprimeness of Semigroups

Barış Albayrak, Didem Yeşil, Didem Karalarlioğlu Camci and Feng Feng

Journal of Mathematics, 2021, vol. 2021, 1-8

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4659756

DOI: 10.1155/2021/4659756

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