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STABILITY OF GORENSTEIN FLAT CATEGORIES

Published online by Cambridge University Press:  09 December 2011

GANG YANG  and
ZHONGKUI LIU
GANG YANG
Affiliation:
School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, P.R. China e-mail: [email protected]
ZHONGKUI LIU
Affiliation:
College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P.R. China e-mail: [email protected]
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Abstract

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A left R-module M is called two-degree Gorenstein flat if there exists an exact sequence of Gorenstein flat left R-modules ⋅⋅⋅ → G2 → G1 → G0 → G−1 → G−2 → ⋅⋅⋅ such that M ≅ Ker(G0 → G−1) and it remains exact after applying H ⊗R- for any Gorenstein injective right R-module H. In this paper we first give some characterisations of Gorenstein flat objects in the category of complexes of modules and then use them to show that two notions of the two-degree Gorenstein flat and the Gorenstein flat left R-modules coincide when R is right coherent.

Keywords

16E1016E3055U15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 177 - 191
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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