Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Published online July 11, 2022

Copyright © The Korean Mathematical Society.

A note on φ-Prufer v-multiplication rings

Xiaolei Zhang

Chengdu Aeronautic Polytechnic

Abstract

In this note, we show that a strongly φ-ring R is a φ-PvMR if and only if any φ-torsion free R-module is φ-w-flat, if and only if any divisible R-module is nonnil-absolutely w-pure, if and only if any h-divisible R-module is nonnil-absolutely w-pure, if and only if any finitely generated nonnil ideal of R is w-projective.

Keywords: φ-PvMRs; φ-w-flat modules; nonnil-absolutely w-pure modules; w-projective modules.

MSC numbers: 13A15; 13F05.

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