On j-flat modules and j-von Neumann regular rings

Abstract

Let R be a commutative ring with a non-zero identity and j be an ideal R. In this paper, we introduce and investigate the concepts of j-torsion modules, j-torsion free modules, j-flat modules and j-von Neumann regular rings. Many examples, characterizations, and properties of these notions are given. Moreover, we use them to characterize reduced rings and ZN-rings. In addition, we present an answer to a question asked by D. D. Anderson and S. Chun \cite[Question 4.4(1)]{Anders}.