On S-maximal Ideals

Yıldız E., Ersoy B. A., Tekir Ü.

ICASEM 4th International Applied Sciences, Engineering and Mathematics Congress, Tekirdağ, Türkiye, 20 - 23 Ekim 2022, ss.18

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Tekirdağ
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.18
  • Marmara Üniversitesi Adresli: Evet

Özet

Let R be a commutative ring with nonzero identity and S be a multiplicatively closed subset of R. An ideal P of R that is disjoint from S is called S-maximal ideal if there exists a fixed s ∈ S such that P ⊆ Q for some ideal Q of R implies either sQ ⊆ P or Q ∩ S ̸= ∅. In this study, first we give some relations between S-prime and S-maximal ideals that are generalizations of prime and maximal ideals, respectively. Moreover, we investigate the behaviour of S-maximal ideals under homomorphisms, rings of fractions, in factor rings.