子空间的并集包含子空间的条件

A condition of the union of subspaces containing a subspace

已有的文献证明了特征为0的域上有限维线性空间的互不包含的子空间的并集不是子空间.考虑这一结论的推广形式,如果一个特征为0的域上线性空间的子空间W包含在有限个子空间的并集中,那么,在这有限个子空间中一定存在一个子空间使得它包含W.对于特征为素数p的域上线性空间,这个结论仅对某些情况成立.并给出了相应的例子.

It was proved that the union of finitely many subspaces which do not contain each other is not a subspace over the field with characteristic 0.This paper consider a generalized case and proves that if a subspace W of a vector space over the field with characteristic 0 is contained in the finitely many subspaces then W must be contained in some subspaces.For a vector space over the field with characteristic p,this conclusion holds only for some particular cases.Some examples are given.