On S-maximal Ideals


Yildiz E., Ersoy B. A., Tekir Ü.

ICASEM IV. Internetional Congress on Applied Sciences, Engineering and Mathematics, Tekirdağ, Turkey, 20 - 23 October 2022, pp.18

  • Publication Type: Conference Paper / Summary Text
  • City: Tekirdağ
  • Country: Turkey
  • Page Numbers: pp.18
  • Yıldız Technical University Affiliated: Yes

Abstract

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.