Exploring the Algebraic and Topological Properties of Semigroups Through Their Prime m-Bi Ideals

Kausar N.

Kragujevac Journal of Mathematics , vol.48, no.3, pp.407-421, 2021 (ESCI)

  • Publication Type: Article / Article
  • Volume: 48 Issue: 3
  • Publication Date: 2021
  • Journal Name: Kragujevac Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.407-421
  • Yıldız Technical University Affiliated: No


We introduce the concepts of the prime m-bi ideal and their associated types in the semigroups. Different characterizations of the semigroups using these m-bi ideals are presented. The forms of the topologies induced by the prime and strongly prime m-bi ideals in the semigroups are also explored. The result shows that either both the conditions of m-regularity and m-intraregularity or existence of pairwise comaximal m-bi ideals in a semigroup is necessary for strongly prime m-bi ideals to induce a topology; whereas the existence of pairwise comaximal m-bi ideals is necessary for the prime m-bi ideals to induce topology on the semigroups. We concluded that the prime m-bi ideals are as important to study the semigroups as the prime bi ideals.