| 强分次环与非分次模范畴 |
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| 引用本文： | 孙建华,李尚志.强分次环与非分次模范畴[J].数学学报,2003,46(6):1103-111. |
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| 作者姓名： | 孙建华 李尚志 |
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| 作者单位： | 1. 扬州大学数学系,扬州,225002
2. 中国科学技术大学数学系,合肥,230026 |
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| 基金项目： | 国家自然科学基金资助项目(10171086) |
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| 摘 要： | 设R是强群G-分次环,日是G的指数有限的子群.本文讨论强分次环R上一般非分次模的一些性质.首先证明一个与非分次R-模和R(H)-子模有关的Maschke-type定理,然后证明从模范畴R(H)-mod到R-mod的函子HomR(H)(R,-)与R(?)R(H)-是一对自然同构的函子以及等价条件.
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| 关 键 词： | G-集分次模 强分次环 函子的自然同构 |
| 文章编号： | 0583-1431(2003)06-1103-08 |
| 修稿时间： | 2000年9月6日 |
Strongly Graded Rings and Ungraded Module Categories |
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| Jian Hua SUN.Strongly Graded Rings and Ungraded Module Categories[J].Acta Mathematica Sinica,2003,46(6):1103-111. |
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| Authors: | Jian Hua SUN |
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| Institution: | Jian Hua SUN
(Department of Mathematics, Yangzhou University, Yangzhou 225002, P. R. China) (E-mail: jhsunyz@yahoo.com.cn)
Shang Zhi LI
(Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China) |
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| Abstract: | Let G be a group. For a strongly G-graded ring R and a subgroup H of G with |G/H| < oo, it is proved that a Maschke-type theorem related to ungraded .R-mod ules and R(H) -submodules holds. Moreover, the natural isomorphic property between the functors HomR(H)(R, -) and R (?)(H) - is characterized. |
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| Keywords: | G-set graded module Strongly graded ring Natural isomorphism of functors |
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