AB-Contexts and Stability for Gorenstein Flat Modules with Respect to Semidualizing Modules
Commutative Algebra
2008-03-10 v1
Abstract
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.
Cite
@article{arxiv.0803.0998,
title = {AB-Contexts and Stability for Gorenstein Flat Modules with Respect to Semidualizing Modules},
author = {Sean Sather-Wagstaff and Tirdad Sharif and Diana White},
journal= {arXiv preprint arXiv:0803.0998},
year = {2008}
}
Comments
22 pages, uses xypic