Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2013; 50(1): 219-229

Printed January 1, 2013

https://doi.org/10.4134/JKMS.2013.50.1.219

Copyright © The Korean Mathematical Society.

On $\phi$-von Neumann regular rings

Wei Zhao, Fanggui Wang, and Gaohua Tang

Sichuan Normal University, Sichuan Normal University, Guangxi Teachers Education University

Abstract

Let $R$ be a commutative ring with $1\neq0$ and let $\mathcal {H} = \{R \,|\,R$ is a commutative ring and $Nil(R)$ is a divided prime ideal$\}$. If $R\in \mathcal {H}$, then $R$ is called a $\phi$-ring. In this paper, we introduce the concepts of $\phi$-torsion modules, $\phi$-flat modules, and $\phi$-von Neumann regular rings.

Keywords: $\phi$-torsion modules, $\phi$-flat modules, $\phi$-von Neumann regular rings

MSC numbers: Primary 13C05, 13C11, 13C12

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