New Results On S-r-ideals in Commutative Rings

This article studies the notion of S-r-ideals in commutative ring H, where S is a multiplicatively closed subset of H. Some basic properties of S-r-ideals are given. Various characterizations of S-r-ideals are presented. Also, S-uz-ring is defined and it is proved that H is an S-uz-ring if and only if every maximal ideal disjoint from S is an S-r-ideal provided S is finite. In addition, the S-r-ideal concept is examined in amalgamation and trivial extension. Finally, S-r-ideals are studied in polynomial rings and it is investigated that when Ax is an S-r-ideal of Hx.