Volume 37 • Number 2 • 2014   • $FP$-Gorenstein Cotorsion Modules Ruiping Lei Abstract. Let $R$ be a ring. In this paper, $FP$-Gorenstein cotorsion modules are introduced and studied. An $R$-module $N$ is said to be $FP$-Gorenstein cotorsion if $Ext_R^1(F,N)=0$ for any finitely presented Gorenstein flat $R$-module $F$. We prove that the class of $FP$-Gorenstein cotorsion modules is covering and preenveloping over coherent rings. $FP$-Gorenstein cotorsion dimension of modules and rings are also studied. Some properties of $FP$-Gorenstein cotorsion modules are given. 2010 Mathematics Subject Classification: 16D50, 16D40, 16E10, 16E30 Full text: PDF