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

By Sean Sather-Wagstaff, Tirdad Sharif, D. White. 2008

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We investigate the properties of categories of GC-flat R-modules where C is a semidualizing module over a commutative noetherian ring R. We prove that the category of all GC-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 GC-flat dimension. We also prove that two procedures for building R-modules from complete resolutions by certain subcategories of GC-flat R-modules yield only the modules in the original subcategories.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/42df20a2312682dbc40f1e6fe5a88164c3cfbac5