Hermite环上矩阵的秩及性质

The Rank and Property of Matrices Over Hermite Ring

设R为Hermite环,A为R上的矩阵,随着对Hermite环的深入研究,近期一维的Hermite环猜想已经得到解决.文章主要总结并讨论A的稳定秩、内秩、行秩之间的关系,以及Hermite环上矩阵的性质.

Let R be a Hermite ring ,A be a matrix over R,with the development of deep re- search,the Hermite ring conjecture in dimension one has been soluted. We induct and discuss the relationship among the stable rank, inner rank and row rank, and the property of matrix over a Bezout domain.