Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON GI-FLAT MODULES AND DIMENSIONS

  • Gao, Zenghui (College of Mathematics Chengdu University of Information Technology)
  • Received : 2012.03.20
  • Published : 2013.01.01
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Abstract

Let R be a ring. A right R-module M is called GI-flat if $Tor^R_1(M,G)=0$ for every Gorenstein injective left R-module G. It is shown that GI-flat modules lie strictly between flat modules and copure flat modules. Suppose R is an $n$-FC ring, we prove that a finitely presented right R-module M is GI-flat if and only if M is a cokernel of a Gorenstein flat preenvelope K ${\rightarrow}$ F of a right R-module K with F flat. Then we study GI-flat dimensions of modules and rings. Various results in [6] are developed, some new characterizations of von Neumann regular rings are given.

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