Stability of Gorenstein X-flat modules
- Authors: Selvaraj C.1, Umamaheswaran A.1
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Affiliations:
- Department of Mathematics
- Issue: Vol 37, No 2 (2016)
- Pages: 193-203
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/197494
- DOI: https://doi.org/10.1134/S199508021602013X
- ID: 197494
Cite item
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 = · · ·→G1 → G0 → G0 → G1 →· · · such that the complex G ⊗RH is exact for each Gorenstein X-injective left R-module H, is themodule M:= im(G0 → G0) a Gorenstein X-flat R-module?
About the authors
C. Selvaraj
Department of Mathematics
Author for correspondence.
Email: selvavlr@yahoo.com
India, Salem Tamil Nadu, 636 011
A. Umamaheswaran
Department of Mathematics
Email: selvavlr@yahoo.com
India, Salem Tamil Nadu, 636 011