EXPLORING THE ALGEBRAIC AND TOPOLOGICAL PROPERTIES OF SEMIGROUPS THROUGH THEIR PRIME m-BI IDEALS

Munir M., KAUSAR N., Anitha K., Mani G., Tehreem T.

Kragujevac Journal of Mathematics, cilt.48, sa.3, ss.407-421, 2024 (ESCI) identifier

  • 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.