Let R be a commutative ring with a nonzero identity and M an R-module. Set ϕ-tor (M)={x∈
M| sx= 0 for some s∈ R∖ Nil (R)}, if ϕ-tor (M)= M then M is called a ϕ-torsion module. An R …

ON φ-VON NEUMANN REGULAR RINGS 1. Introduction Let R be a commutative ring with 1 =
0 and Nil(R) be its set of nilpotent elemen Page 1 J. Korean Math. Soc. 50 (2013), No. 1, pp …

Let R be a commutative ring with non-zero identity and let NN (R)={I| I is a nonnil ideal of R}.
Let M be an R-module and let ${\phi}-tor (M)=\{x {\in} M {\mid} Ix= 0\text {for some} I {\in} NN …

This paper introduces and studies the ϕ-uS-flat (resp., nonnil-uS-injective) modules, which
are a generalization of both ϕ-flat modules and uS-flat modules (resp., both nonnil-injective …

In this paper, we generalize, with respect to the w-operation, the notions of FI-injective and FI-
flat modules introduced by L. Mao and N. Ding. Let R be a ring. An R-module M is called w …

Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be (m,
n)-injective if Ext1 (P, M)= 0 for any (m, n)-presented right R-module P; M is said to be (m, n) …

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 commutative ring with nonzero identity. An $ R $-module $ M $ is called $\phi
$-P-flat if $ x\in\Ann (s) M $ for every non-nilpotent element $ s\in R $ and $ x\in M $ such …

In this article, we introduce the concept of IFP-flat (resp., IFP-injective) modules as nontrivial
generalization of flat (resp., injective) modules. We investigate the properties of these …

Abstract A left R-module M is said to be fp-injective if, for every monomorphism K→ L with K
and L finitely presented left R-modules, Hom (L, M)→ Hom (K, M) is an epimorphism. A right …