2008/03/06 by Sean Sather-Wagstaff, Sather-Wagstaff, Sean, Tirdad Sharif +3
Mathematics · Physics and Astronomy · #13C05 #13C11 #13D02 #13D05 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Nonlinear Waves and Solitons #math.AC #msc:13C05 #msc:13C11 #msc:13D02 #msc:13D05
paper · pdf · doi:10.48550/arxiv.0803.0998
22 pages, uses xypic
arxiv created 2008/03/06 · openalex publication_date 2008/03/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.