Gorenstein相对上同调

Gorenstein Relative Cohomology

设M,N是左R-模.证明了如果M的X-Gorenstein投射维数有限,N的Y-Gorenstein内射维数有限,则利用M真的左X-Gorenstein投射分解定义的相对上同调群Ext（X-GP（M,N））^n与N真的右Y-Gorenstein内射分解定义的相对上同调群Ext（Y-GI（M,N））^n同构.

Let M, N be left R-modules. We proved that if both the X-Gorenstein projective dimension of M and the Y-Gorenstein injective dimension of N were finite, then the relative cohomology group Ext（X-GP（M,N））^n defined by a proper left X-Gorenstein projective resolution of M and the relative cohomology group Ext（Y-GI（M,N） defined by a proper right Y-Gorenstein injective resolution of N were isomorphic.