| Hopf Galois扩张与Hopf模结构定理 |
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| 引用本文： | 陈惠香.Hopf Galois扩张与Hopf模结构定理[J].数学学报,1995,38(2):228-233. |
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| 作者姓名： | 陈惠香 |
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| 作者单位： | 扬州大学师范学院数学系 |
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| 摘 要： | 设Ｈ是域ｋ上任意的Ｈｏｐｆ代数。本文首先讨论了右Ｈ＿扩张Ａ／Ａ￣（ｃｏＨ）与Ｈｏｐｆ模范畴，给出了Ａ／Ａ￣（ｃｏＨ）为右Ｈ－Ｇａｌｏｉｓ扩张的充分必要条件和Ｈｏｐｆ模范畴满足结构定理的若干等价条件．然后我们讨论了不可约作用与除环的Ｇａｌｏｉｓ扩张．
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| 关 键 词： | Hopf上模代数，Smash积，Hopf模，Galois扩张 |
| 收稿时间： | 1992-10-26 |
| 修稿时间： | 1993-3-23 |
Hopf Galois Extensions and Structure Theorems of Hopf Modules |
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| Chen Huixiang.Hopf Galois Extensions and Structure Theorems of Hopf Modules[J].Acta Mathematica Sinica,1995,38(2):228-233. |
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| Authors: | Chen Huixiang |
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| Institution: | Chen Huixiang(Department of Mathematics, yangzhou University Teachers College,Yangzhou 225002,China) |
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| Abstract: | Let H be an arbitrary Hopf algebra over a field k.At first,we deal with the right H-extension A/A￣(coH) and the Hopf module category In this paper we give several sufficientand necessary conditions for A/A￣(coH) being right H-Galois extension, and several equivalentconditions for the Hopf module category satisfying the structure theorem. Then we discussthe irreducible actions and the Galois extensions of division rings. |
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| Keywords: | Hopf comodule algebra Smash product Hopf module Galois extension |
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