CAJ | 학술논문

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.
주요운용향량공간적일사성질화특점,인진료2-겁대자공간개념,종여자공간、유수、동구영사등방면대2-겁대자공간적성질진행료연구,주요득출료3개결론：（1）설V시수역F상적n（n≥2）유향량공간,M2≤.M1≤.V,칙dimM2=n-2.（2）설V시수역F상적향량공간,약M2≤.M1≤.V당차부당M2시2유자공간적여자공간.（3）f시향량공간W→V적일개동구영사,칙W적일개2-겁대자공간W2통과동구영사f야시V적일개2-겁대자공간.
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.