In this study, we introduce the concepts of $ S $-prime submodules and\$ S $%-torsion-free
modules, which are generalizations of prime submodules and torsion-free modules …

Let R be a commutative ring with identity and let 𝒬 be the set of finitely generated
semiregular ideals of R. A 𝒬-torsion-free R-module M is called a Lucas module if Ext R 1 …

In this article, we introduce the concepts of graded $ s $-prime submodules which is a
generalization of graded prime submodules. We study the behavior of this notion with …

Let R be a commutative ring with identity and S a multiplicative subset of R. The aim of this
paper is to study the class of commutative rings in which every S-flat module is flat (resp …

Let $ R $ be a ring and $ S $ a multiplicative subset of $ R $. Then $ R $ is called a uniformly
$ S $-Noetherian ($ u $-$ S $-Noetherian for abbreviation) ring provided there exists an …

Let $ R $ be a ring and $ S $ a multiplicative subset of $ R $. An $ R $-module $ T $ is called
$ u $-$ S $-torsion ($ u $-always abbreviates uniformly) provided that $ sT= 0$ for some …

Let D be an integral domain with quotient field K, X be an indeterminate over D, K [X] be the
polynomial ring over K, n≥ 2 be an integer, K [θ]= K [X]/(X n), where θ= X+(X n), and R n …

In this article, we introduce two new classes of modules over a ϕ-ring that generalize the
classes of coherent modules and Noetherian modules. We next study the possible transfer …

Let R be a commutative ring. If the nilpotent radical N il (R) of R is a divided prime ideal, then
R is called a ϕ-ring. In this paper, we first distinguish the classes of nonnil-coherent rings …

In this paper, we introduce and study the class of $\phi $-$ w $-flat modules which are
generalizations of both $\phi $-flat modules and $ w $-flat modules. The $\phi $-$ w $-weak …