Geodesic
Exploring the Algebraic and Topological Properties of Semigroups Through Their Prime $m$-Bi Ideals Exploring the Algebraic and Topological Properties of Semigroups Through Their Prime $m$-Bi Ideals
Kragujevac Journal of Mathematics, Tome 48 (2024) no. 3, p. 407 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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.
DOI : 10.46793/KgJMat2403.407M
Classification : 20M17, 22A15
Keywords: prime m-bi ideals, m-regularity, comaximal ideals, topology 
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     title = {Exploring the {Algebraic} and {Topological} {Properties} of {Semigroups} {Through} {Their} {Prime} $m${-Bi} {Ideals} {Exploring} the {Algebraic} and {Topological} {Properties} of {Semigroups} {Through} {Their} {Prime} $m${-Bi} {Ideals}},
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Mohammad Munir; Nasreen Kausar; K. Anitha; Gunaseelan Mani; Tehreem . Exploring the Algebraic and Topological Properties of Semigroups Through Their Prime $m$-Bi Ideals Exploring the Algebraic and Topological Properties of Semigroups Through Their Prime $m$-Bi Ideals. Kragujevac Journal of Mathematics, Tome 48 (2024) no. 3, p. 407 . doi: 10.46793/KgJMat2403.407M

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