[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2013.50.1.203

ON GI-FLAT MODULES AND DIMENSIONS

Gao, Zenghui (College of Mathematics Chengdu University of Information Technology)

Publication Information

Journal of the Korean Mathematical Society / v.50, no.1, 2013 , pp. 203-218 More about this Journal

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.

Keywords

Gorenstein injective module; GI-flat module; GI-flat dimension; n-FC ring; Gorenstein flat preenvelope;

Citations & Related Records

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