Stability of Gorenstein X-flat modules

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• 作者：C. Selvaraj ; A. Umamaheswaran
• 刊名：Lobachevskii Journal of Mathematics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：37
• 期：2
• 页码：193-203
• 全文大小：667 KB
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• 作者单位：C. Selvaraj (1)
  A. Umamaheswaran (1)
  
  1. Department of Mathematics, Periyar University, Salem Tamil Nadu, 636 011, India
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Analysis
  Geometry
  Mathematical Logic and Foundations
  Probability Theory and Stochastic Processes
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1818-9962

文摘

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?