Exploring the Algebraic and Topological Properties of Semigroups Through Their Prime $m$-Bi Ideals
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Authors: M. MUNIR, N. KAUSAR, K. ANITHA AND G. MANI AND TEHREEM
DOI: 10.46793/KgJMat2403.407M
Abstract:
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.
Keywords:
prime m-bi ideals, m-regularity, comaximal ideals, topology.
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