华的一个定理在单Artin环上的推广

摘要

本文研究了单Artin环上矩阵的内秩与算术距离.利用Wedderburn-Artin定理,获得了单Artin环上矩阵的保粘切与对应的表示矩阵的一个等价关系,推广了华的体上长方矩阵几何基本定理到单Artin环.%In this paper, we study the inner rank and the arithmetic distance of the matrix over simple Artin ring. By using Wedderburn-Artin theorem, we obtain that adjacency preserving of the matrices over simple Artin ring is equivalent to its representation matrix, and extend Hua's theorem on the geometry of the rectangular matrices to a simple Artin ring.