| 摘要: |
| 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. |
| 关键词: 凝聚环 Gorenstein平坦模 Gorenstein余挠模 |
| DOI： |
| 分类号:O154.2 |
| 基金项目:Supported by the Natural Science Fund for Colleges and Universities in Jiangsu Province (15KJB110023) and the School Foundation of Yangzhou University (2015CJX002). |
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| GORENSTEIN FLAT(COTORSION) DIMENSIONS AND HOPF ACTIONS |
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MENG Fan-yun
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School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
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| Abstract: |
| 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. |
| Key words: coherent ring Gorenstein fieldat module Gorenstein cotorsion module |
