Studying semigroups using the properties of their prime m-ideals

Munir M., KAUSAR N., Davvaz B., Gulistan M., Gulzar M.

Bulletin of Irkutsk State University, Series Mathematics, vol.4, pp.109-125, 2021 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4
  • Publication Date: 2021
  • Doi Number: 10.26516/1997-7670.2020.34.109
  • Journal Name: Bulletin of Irkutsk State University, Series Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.109-125
  • Keywords: Completely prime m-ideals, Irreducible m-ideals, Maximal m-ideals, Strongly Irreducible m-ideals, Strongly prime m-ideals
  • Yıldız Technical University Affiliated: No

Abstract

In this article, we present the idea of m-ideals, prime m-ideals and their associated types for a positive integer m in a semigroup. We present different chrarc- terizations of semigroups through m-ideals. We demonstrate that the ordinary ideals, and their relevent types differ from the m-ideals and their assocated types by presenting concrete examples on the maximal, irreducible and strongly irreducible m-ideals. We conclude from the study that the introduction of the m-ideal will explore new fields of studies in semigroups and their applications.