EXPLORING THE ALGEBRAIC AND TOPOLOGICAL PROPERTIES OF SEMIGROUPS THROUGH THEIR PRIME m-BI IDEALS
Kragujevac Journal of Mathematics, cilt.48, sa.3, ss.407-421, 2024 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 48 Sayı: 3
- Basım Tarihi: 2024
- Doi Numarası: 10.46793/kgjmat2403.407m
- Dergi Adı: Kragujevac Journal of Mathematics
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
- Sayfa Sayıları: ss.407-421
- Anahtar Kelimeler: comaximal ideals, m-regularity, prime m-bi ideals, topology
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
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.