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STABILITY OF GORENSTEIN FLAT MODULES

Published online by Cambridge University Press:  09 December 2011

SAMIR BOUCHIBA  and
MOSTAFA KHALOUI
SAMIR BOUCHIBA
Affiliation:
Department of Mathematics, University Moulay Ismail, Meknes 50000, Morocco e-mail: [email protected]; [email protected]
MOSTAFA KHALOUI
Affiliation:
Department of Mathematics, University Moulay Ismail, Meknes 50000, Morocco e-mail: [email protected]; [email protected]
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Abstract

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Sather-Wagstaff et al. proved in [8] (S. Sather-Wagsta, T. Sharif and D. White, Stability of Gorenstein categories, J. Lond. Math. Soc.(2), 77(2) (2008), 481–502) that iterating the process used to define Gorenstein projective modules exactly leads to the Gorenstein projective modules. Also, they established in [9] (S. Sather-Wagsta, T. Sharif and D. White, AB-contexts and stability for Goren-stein at modules with respect to semi-dualizing modules, Algebra Represent. Theory14(3) (2011), 403–428) a stability of the subcategory of Gorenstein flat modules under a procedure to build R-modules from complete resolutions. In this paper we are concerned with another kind of stability of the class of Gorenstein flat modules via-à-vis the very Gorenstein process used to define Gorenstein flat modules. We settle in affirmative the following natural question in the setting of a left GF-closed ring R: Given an exact sequence of Gorenstein flat R-modules G = ⋅⋅⋅ G2G1G0G−1G−2 ⋅⋅⋅ such that the complex H ⊗RG is exact for each Gorenstein injective right R-module H, is the module M:= Im(G0 → G−1) a Gorenstein flat module?

Keywords

13D0213D0513D0716E0516E10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 169 - 175
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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