| 引用本文： |
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刘秀,郭龙先,韦华全.算子群与直积分解[J].广西科学,2011,18(1):1-4. [点击复制]
- LIU Xiu,GUO Long-xian,WEI Hua-quan.Operator Groups and Direct Product Decomposition[J].Guangxi Sciences,2011,18(1):1-4. [点击复制]
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| 摘要: |
| 引入广义同态映射的定义,将算子群的算子集进行扩充,得到一些有关算子群的结果,推广了经典的Schur定理、Fitting定理和Krull-Schmidt定理等. |
| 关键词: 群 算子群 广义同态 反同态 反同构 直积 |
| DOI： |
| 投稿时间：2010-12-12修订日期：2010-12-24 |
| 基金项目:国家自然科学基金项目(10961007);云南省高等学校精品课程-《高等代数》项目;广西研究生教育创新计划项目(2007106030701M13)资助 |
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| Operator Groups and Direct Product Decomposition |
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LIU Xiu1, GUO Long-xian1, WEI Hua-quan2
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| (1.Department of Mathematics, Zhaotong Teacher′s College, Zhaotong, Yunnan, 657000, China;2.School of Mathmatical Sciences, Guangxi Teachers Education University, Nanning, Guangxi, 530023, China) |
| Abstract: |
| By using the concept of generalized homomorphism, we extent the operator set of operator groups, obtain some results obout operator groups and generalize the classical theory of operator groups, such as the theorems of Schur, Fitting and Krull-Schmidt. |
| Key words: group operator group generalized homomorphism anti-homomorphism anti-isomorphism direct product |
