Gorenstein平坦(余挠)维数和Hopf作用
GORENSTEIN FLAT(COTORSION) DIMENSIONS AND HOPF ACTIONS

设H是域k上的有限维Hopf代数，A是左H-模代数.本文研究了Gorenstein平坦（余挠）维数在A-模范畴和A#H-模范畴之间的关系.利用可分函子的性质，证明了（1）设A是右凝聚环，若A#H/A可分且φ：A→A#H是可裂的（A，A）-双模同态，则l：Gwd（A）=l：Gwd（A#H）；（2）若A#H/A可分且φ：A→A#H是可裂的（A，A）-双模同态，则l：Gcd（A）=l：Gcd（A#H），推广了斜群环上的结果.
In this paper, we study the relationship of Gorenstein fieldat (cotorsion) dimensions between A-Mod and A#H-Mod. Using the properties of separable functors, we get that (1) Let A be a right coherent ring, assume that A#H/A is separable and φ:A→A#H is a splitting monomorphism of (A, A)-bimodules, then l:Gwd(A)=l:Gwd(A#H); (2) Assume that A#H/A is separable and φ:A→A#H is a splitting monomorphism of (A, A)-bimodules, then l:Gcd(A)=l:Gcd(A#H), which generalized the results in skew group rings