中文摘要：

讨论有限维代数Ai的张量代数n×i=1Ai上的Gorentein投射维数有限的模范畴和Ai上的Gorenstein投射维数有限的模范畴之间的关系并有如下结论：对于任意n（n为任意正整数）个有限维k-代数Ai（i=1,2,…,n），如果G-p∞（n×i=1Ai）在n×i=1Ai-mod反变有限，那么G-p∞（Ai）在Ai-mod中反变有限。

英文摘要：

In this paper,we study the relationship between the subcategory consists of the modules n with finitely Gorenstein projective dimension in n×i=1A-mod and the subcategories of the modules withfinitely Gorenstein projective dimension in Ai-mod. We have the following conclusion：For any andn〉0 finitely dimensional k-algebras Ai （i = 1,2, L n）, If G-p∞ （×pi=1Ai）is contravariantly finite in ×i=1Ai-mod,the G-p∞is contravariantly finite in Ai-mod.