V_n(R^+)中半线性生成子空间的基与维数

Base and Dimension of Semilinear Generated Subspace of V_n(R^+)

在交换的零和自由半环上,首先讨论了半线性空间V_n中向量组线性相关性的一些性质,并给出向量组中极大线性无关组所含向量个数相同的条件.其次通过对半环<R^+,+,.,0,1>上生成子空间基的讨论,给出了向量组的极大线性无关组含相同向量个数的条件.最后对<R^+,+,.,0,1>上生成子空间的维数进行详细讨论并给出相应的结果.

In this paper,we first discuss some properties of linear relation of vector groups in semilinear space V_n over zerosumfree semirings,and give some conditions that each maximum linear independence group has the same number of elements.Then we discuss the bases of generated subspace over semiring<R^+,+,·,0,1>,and prove that each maximum linear independence group has the same number of elements.Finally,we study the dimension of generated subspace over(R^+,+,·,0,1>and the corresponding results.