非交换主理想整环上分块矩阵的秩

The Rank of Partitioned Matrices over Non-commutative Principal Ideal Domain

本文从非交换主理想整环Ｒ上矩阵Ａ的秩与它在Ｒ所嵌入的商除环Ｋ上的秩间的关系着手，证得了Ｒ上分块矩阵秩的一些结果，因此也解决了［１］中关于ｐ￣一除环上矩阵秩的一个猜想．

Using the fact that a non- commutative principal ideal domain can be imbedded in a quotient division ring,we prove some results on the rank of partitioned matrices over a non-commutative principal ideal domain, and then solve the conjecture for the rank of matrices over a p-division ring in [1].