Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2014; 51(1): 173-187

Printed January 1, 2014

https://doi.org/10.4134/BKMS.2014.51.1.173

Copyright © The Korean Mathematical Society.

On Gorenstein cotorsion dimension over GF-closed rings

Zenghui Gao

Chengdu University of Information Technology

Abstract

In this article, we introduce and study the Gorenstein cotorsion dimension of modules and rings. It is shown that this dimension has nice properties when the ring in question is left GF-closed. The relations between the Gorenstein cotorsion dimension and other homological dimensions are discussed. Finally, we give some new characterizations of weak Gorenstein global dimension of coherent rings in terms of Gorenstein cotorsion modules.

Keywords: Gorenstein flat module, Gorenstein cotorsion dimension, weak Gorenstein global dimension, GF-closed ring

MSC numbers: 16E10, 16E30, 16E50

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