On Φ-von Neumann regular rings

Abstract

Let R be a commutative ring with 1≠ 0 and let H = {R|R is a commutative ring and Nil(R) is a divided prime ideal}. If R∈ H, then R is called a Φ- ring. In this paper, we introduce the concepts of Φ-torsion modules, Φ- flat modules, and Φ- von Neumann regular rings. © 2013 The Korean Mathematical Society.