2-Maximal Subspaces of Vector Spaces

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.