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