| 向量空间的2-极大子空间 |
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| 引用本文： | 徐周亚,吴洪梅,贾华林,刘熠.向量空间的2-极大子空间[J].内江师范学院学报,2012,27(2):22-24. |
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| 作者姓名： | 徐周亚 吴洪梅 贾华林 刘熠 |
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| 作者单位： | 内江师范学院数学与信息科学学院,四川内江,641100 |
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| 基金项目： | 四川省教育厅资助科研项目，内江师范学院大学生科研项目 |
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| 摘 要： | 主要运用向量空间的一些性质和特点,引进了2-极大子空间概念,从余子空间、维数、同构映射等方面对2-极大子空间的性质进行了研究,主要得出了3个结论：（1）设V是数域F上的n（n≥2）维向量空间,M2≤.M1≤.V,则dimM2=n-2.（2）设V是数域F上的向量空间,若M2≤.M1≤.V当且仅当M2是2维子空间的余子空间.（3）f是向量空间W→V的一个同构映射,则W的一个2-极大子空间W2通过同构映射f也是V的一个2-极大子空间.
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| 关 键 词： | 向量空间 2-极大子空间 余子空间 维数 同构映射 |
2-Maximal Subspaces of Vector Spaces |
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| XU Zhou-ya,WU Hong-mei,JIA Hua-lin,LIU Yi.2-Maximal Subspaces of Vector Spaces[J].Journal of Neijiang Teachers College,2012,27(2):22-24. |
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| Authors: | XU Zhou-ya WU Hong-mei JIA Hua-lin LIU Yi |
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| Institution: | (College of Mathematics and Information Science,Neijiang Normal University,Neijiang,Sichuan 641100,China) |
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| Abstract: | Limitations of the existing literature about the vector space lie mostly in the research of the nature of complemented subspaces.In order to solve this problem,the nature and some features of vector space are put under examination and the concept of 2-maximal subspaces of a vector space is introduced.The properties of 2-maximal subspaces are investigated from the perspectives of complemented subspaces,dimension and isomorphic mapping,which brings forth three major conclusions:(1)Let V be a n-dimensional vector space in domain F,given that M2≤·M1≤·V,then M2=n-2 will be true.(2)Let V be a vector space in domain F,if M2≤·M1≤·V,When,and only when M2 is a complemented subspaces of 2 dimension subspace.(3)Given that f is an isomorphic mapping of a vector space W→V,then one of the 2-maximal subspaces of W,suppose W2,must also be a 2-maximal subspace of V through the isomorphic mapping f. |
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| Keywords: | vector space 2-maximal subspace complemented subspace dimension isomorphic mapping |
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