论文标题
在稳定范围内矩阵
On stable range one matrices
论文作者
论文摘要
对于2 x 2矩阵，我们证明了左稳定范围1元素的特征定理，我们表明稳定范围1的属性在元素级别上是左右对称（也是），我们表明，所有零行（或一个零行（或零列）的所有矩阵在bezout contable contable环上均具有稳定范围1。 Jacobson引理稳定范围1元素。最后，我们给出了一个不干净的交换稳定范围1积分2 x 2矩阵的示例。
For 2 by 2 matrices over commutative rings, we prove a characterization theorem for left stable range 1 elements, we show that the stable range 1 property is left-right symmetric (also) at element level, we show that all matrices with one zero row (or zero column) over Bezout rings have stable range 1. Using diagonal reduction, we characterize all the 2 by 2 integral matrices which have stable range 1 and discuss additional properties including Jacobson Lemma for stable range 1 elements. Finally, we give an example of exchange stable range 1 integral 2 by 2 matrix which is not clean.
