范畴X与G(X,Y,Z)的关系

The relations between the categories X and G(X,Y,Z)

范畴G(X,Y,Z)包含了Gorenstein投射模、Gorenstein内射模、强Gorenstein平坦模和Gorenstein FP-内射模等众多模类,其中范畴X具有举足轻重的作用.这是因为X是G(X,Y,Z)的生成子和余生成子.通过研究维数,证明当模M的G(X,Y,Z)-分解维数有限时,它有特殊的G(X,Y,Z)-预盖;当模M的X-分解维数有限时,M的G(X,Y,Z)-分解维数等于它的X-分解维数.

The category G(X,Y,Z)contains Gorenstein projective modules,Gorenstein injective modules,strongly Gorenstein flat modules,Gorenstein FP-injective modules and so on.The category X plays an important role in the category G(X,Y,Z).That is because X is a generator and cogenerator for G(X,Y,Z).By studying relevant dimensions,it is proved that if the G(X,Y,Z)-resolution dimension of M is finite,then it has a special G(X,Y,Z)-precover;if the X-resolution dimension of M is finite,then the G(X,Y,Z)-resolution dimension of M is equal to the X-resolution dimension of M.