Stability of Gorenstein X-flat modules
C Selvaraj, A Umamaheswaran - Lobachevskii Journal of Mathematics, 2016 - Springer
Lobachevskii Journal of Mathematics, 2016•Springer
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⊗ RH is exact for each Gorenstein X-injective left R-module H, is themodule …
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⊗ RH is exact for each Gorenstein X-injective left R-module H, is themodule …
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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