中文摘要：

探讨了Hopf代数上的交叉积A#σH和其子代数A之间的有限表现维数的关系；研究了交叉积A#σH成为n—Gorenstein代数的条件．所得结果与著名的Gorenstein对称猜想有一定的联系．

英文摘要：

The relationship of finitely presented dimensions between the crossed product A#σH and its subalge-bra A was given. Conditions for the crossed product A#σH being an n-Gorenstein algebra was also studied. The obtained results had some connections with the famous Gorenstein symmetric conjecture.