Stability of Gorenstein  X -flat modules

C. Selvaraj; A. Umamaheswaran

doi:10.1134/S199508021602013X

Stability of Gorenstein X-flat modules

Authors: Selvaraj C.¹, Umamaheswaran A.¹
Affiliations:
1. 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

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract
About the authors
References
Statistics

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?

Keywords

X-injective module, X-flat module, Gorenstein X-flat module, GXF-closed ring

About the authors

C. Selvaraj

Department of Mathematics

Author for correspondence.
Email: selvavlr@yahoo.com
India, Salem Tamil Nadu, 636 011

A. Umamaheswaran