Gorenstein 相对上同调

摘要

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 n X-GP(M,N )defined by a proper left X-Gorenstein projective resolution of M and the relative cohomology group Ext n Y-GI(M,N )defined by a proper right Y-Gorenstein injective resolution of N were isomorphic.%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 n X-GP(M,N )与 N 真的右 Y-Gorenstein 内射分解定义的相对上同调群 Ext n Y-GI(M,N )同构。