On s-maximal ideals

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.