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Gorenstein Flat Covers of Modules over Gorenstein Rings

✍ Scribed by Edgar Enochs; Jinzhong Xu

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 220 KB
Volume: 181
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0121

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✦ Synopsis

A left and right Noetherian ring R is called Gorenstein if both R and R have R R finite injective dimensions. These rings were studied by Bass for the commutative case and Iwanaga for the noncommutative case. In this paper, we define Gorenstein flat modules over a Gorenstein ring. These modules are a generalization of flat modules. After discussing the properties of modules over a Gorenstein ring, we prove that every module over a Gorenstein ring has a Gorenstein flat cover or a minimal right approximation by a Gorenstein flat module in Auslander and Reiten's terminology.

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