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Stability of Gorenstein X-flat modules

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Abstract

In this paper we introduce the notion of Gorenstein X-flat R-module and study a kind of stability of the class of Gorenstein X-flat R-modules. A ring R is called right GXF-closed if the class of all Gorenstein X-flat right R-modules is closed under extensions. We give an answer for the following natural question in the setting of a right GXF-closed ring R: Given an exact sequence of Gorenstein X-flat right R-modules G = · · ·→G 1 → G 0 → G 0 → G 1 →· · · such that the complex G ⊗ R H is exact for each Gorenstein X-injective left R-module H, is themodule M:= im(G 0 → G 0) a Gorenstein X-flat R-module?

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Authors and Affiliations

  1. Department of Mathematics, Periyar University, Salem Tamil Nadu, 636 011, India

    C. Selvaraj & A. Umamaheswaran

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  1. C. Selvaraj
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  2. A. Umamaheswaran
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Correspondence to C. Selvaraj.

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Submitted by S. N. Tronin

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Selvaraj, C., Umamaheswaran, A. Stability of Gorenstein X-flat modules. Lobachevskii J Math 37, 193–203 (2016). https://doi.org/10.1134/S199508021602013X

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  • DOI: https://doi.org/10.1134/S199508021602013X

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