Journal of the
Korean Mathematical Society JKMS

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 $K\ra F$ of a right $R$-module $K$ with $F$ flat. Then we study GI-flat dimensions of modules and rings. Various results in \cite{DC93} 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

MSC numbers: 16E30, 16E10, 16E50