摘要
本文结果是：设Ａ是φ－满射环Ｒ上的非拟纯量可逆ｎ×ｎ矩阵，βｊ，γｊ（尔≤ｊ≤ｎ）是Ｒ中任意元素，它们满足Πｎｊ＝１βｊγｊ＝ｄｅｔＡ，则存在ｎ阶阵Ｂ和Ｃ满足ＰＡＰ－１＝ＢＣ，其中Ｂ是下三角阵，Ｃ是上三角阵，Ｐ∈ＧＬｎ（Ｒ）．进一步，可以取Ｂ使βｊ（１≤ｊ≤ｎ）位于Ｂ的主对角线上，同时可以取Ｃ使γｊ（１≤ｊ≤ｎ）位于Ｃ的主对角线上．
In this paper. we extend the main theorem in [1]. Our main result is :Let A be a non -near scalar invertible n×n matrix over φ-surjective ring R. Let βj and γj(1<j<n) be any elements of R such such that A. Then there exist n×n matrices B such C such that PAP-1=BC. is a lower triangular and C is simultaneously upper triangularizable P∈GLn (R). Furthermore B and C can be chosen so that the elements in the main diagonal line of B are B are β1…βn and of C are γ1…γn.
