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

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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.

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Authors and Affiliations

  1. Department of Mathematics, North Dakota State University, Dept 2750, PO Box 6050, Fargo, ND, 58108-6050, USA

    Sean Sather-Wagstaff

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    Tirdad Sharif

  3. Department of Mathematical & Statistical Sciences, University of Colorado Denver, Campus Box 170, P.O. Box 173364, Denver, CO, 80217-3364, USA

    Diana White

Authors
  1. Sean Sather-Wagstaff
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  2. Tirdad Sharif
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  3. Diana White
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Correspondence to Sean Sather-Wagstaff.

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TS is supported by a grant from IPM, (No. 83130311).

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Sather-Wagstaff, S., Sharif, T. & White, D. AB-Contexts and Stability for Gorenstein Flat Modules with Respect to Semidualizing Modules. Algebr Represent Theor 14, 403–428 (2011). https://doi.org/10.1007/s10468-009-9195-9

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