Let $ R $ be a commutative ring with identity and $ N (R) $ and $ J\left (R\right) $ denote the
nilradical and the Jacobson radical of $ R $, respectively. A proper ideal $ I $ of $ R $ is …

This paper deals with Krasner hyperrings as an important class of algebraic hyperstructures.
We investigate some properties of r‐hyperideals in commutative Krasner hyperrings. Some …

In this study, we present generalizations of the concept of r-ideals in commutative rings with
a nonzero identity. Let R be a commutative ring with 0≠ 1 and L (R) be the lattice of all …

Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, we
introduce the concept of r-Artinian modules which is a new generalization of Artinian …

Let R be a commutative ring with nonzero identity. In this paper, we introduce and
investigate a new class of ideals that is closely related to the class of r-ideals. A proper ideal …

We investigate some properties of n-submodules. More precisely, we find a necessary and
sufficient condition for every proper submodule of a module to be an n-submodule. Also, we …

Let R be a commutative ring with 1≠ 0 and M a unital R-module. M is said to satisfy Property
(A) if for each finitely generated ideal J of R contained in ZR (M), there exists 0≠ m∈ M such …

In this article, we are interested in uniformly pr-ideals with order≤ 2 (which we call 2 r-
ideals) introduced by Rabia Üregen in [On uniformly pr-ideals in commutative rings, Turkish …

In this paper we introduce and study a class of ideals between z-ideals and z°-ideals (= d-
ideals) namely zr-ideals. A zr-ideal is az-ideal which is at the same time an r-ideal (an ideal I …

r-Ideals of Commutative Ordered Semigroups 1 Introduction Page 1 International Journal of
Mathematics and Computer Science, 19(2024), no. 3, 653–660 M CS r-Ideals of Commutative …