We introduce a new class of rings which is closely related to the class of strong Mori
domains which was introduced by the second author. Let H={R| R is a commutative ring with …

Let R be a commutative ring with prime nilradical Nil (R) and M an R-module. Define the
map 𝜙: R→ R Nil (R) by ${\phi}(r)=\frac {r}{1} $ for r∈ R and 𝜓: M→ M Nil (R) by …

In this paper, we introduce the new concept of nonnil-commutative diagrams (resp., nonnil-
projective modules) as a generalization of commutative diagrams (resp., projective …

ON NONNIL-EXACT SEQUENCES AND NONNIL-COMMUTATIVE DIAGRAMS 1. Introduction
Throughout this paper, it is assumed that all rings ar Page 1 J. Korean Math. Soc. 60 (2023) …

In this paper, we introduce the concept of NN-torsion-free modules (respectively, NN-
injective modules) as a generalization of nonnil-torsion-free modules (respectively, injective …

Let R be a commutative ring and Nil (R) denote the set of nilpotent elements of R. In this
paper, we investigate two generalizations of exact sequences, ϕ-exact sequences and N …

Let R be a commutative ring and S a given multiplicative closed subset of R. In this paper,
we introduce the new concept of S-torsion exact sequences (respectively, S-torsion …

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 …

Recently, Zhao, Wang, and Pu introduced and studied new concepts of nonnil-commutative
diagrams and nonnil-projective modules. They proved that an R-module that is nonnil …

An endomorphism α of a ring R is called weak reversible if whenever the product of any two
elements of a ring R, ab, is a nilpotent element of R, then so is the bα (a). A ring R is called …