Studying semigroups using the properties of their prime m-ideals

Munir M., KAUSAR N., Davvaz B., Gulistan M., Gulzar M.

Bulletin of Irkutsk State University, Series Mathematics, cilt.4, ss.109-125, 2021 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.26516/1997-7670.2020.34.109
  • Dergi Adı: Bulletin of Irkutsk State University, Series Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.109-125
  • Anahtar Kelimeler: Completely prime m-ideals, Irreducible m-ideals, Maximal m-ideals, Strongly Irreducible m-ideals, Strongly prime m-ideals
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this article, we present the idea of m-ideals, prime m-ideals and their associated types for a positive integer m in a semigroup. We present different chrarc- terizations of semigroups through m-ideals. We demonstrate that the ordinary ideals, and their relevent types differ from the m-ideals and their assocated types by presenting concrete examples on the maximal, irreducible and strongly irreducible m-ideals. We conclude from the study that the introduction of the m-ideal will explore new fields of studies in semigroups and their applications.