AB-Contexts and Stability for Gorenstein Flat Modules with Respect to Semidualizing Modules

Details AB-Contexts and Stability for Gorenstein Flat Modules with Respect to Semidualizing Modules AB-Contexts and Stability for Gorenstein Flat Modules with Respect to Semidualizing Modules

2008-03-06

arxiv.org/abs/0803.0998v1

Mathematics

Commutative Algebra

22 pages, uses xypic

Scientific paper

We investigate the properties of categories of G_C-flat R-modules where C is a semidualizing module over a commutative noetherian ring R. We prove that the category of all G_C-flat R-modules is part of a weak AB-context, in the terminology of Hashimoto. In particular, this allows us to deduce the existence of certain Auslander-Buchweitz approximations for R-modules of finite G_C-flat dimension. We also prove that two procedures for building R-modules from complete resolutions by certain subcategories of G_C-flat R-modules yield only the modules in the original subcategories.

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