中文摘要：

研究了两类模：GI平坦模和GF挠模,其中,GI表示Gorenstein内射模,GF表示Gorenstein平坦模;刻画了环的两个同调维数,即Gorenstein内射模的最大平坦维数和模的最大GF挠维数.同时也研究了这些模类和同调维数之间的关系.

英文摘要：

Two classes of modules were studied：GI-flat and GF-torsion modules,where GI stands for Gorenstein injective modules and GF for Gorenstein flat modules. Two homological dimensions for a ring were investigated,the supremum of the flat dimension of Gorenstein injective modules and the supremum of the GF-torsion dimension of all modules.The relation between these classes of modules and the homological dimensions was also studied.