(强)Kasch n阶三角矩阵环的等价刻画

Equivalent characterization of (strong) Kasch triangular matrix ring of order n

设T是一个n阶三角矩阵环,其中n≥2是一个正整数。给出了T的极大理想与极小理想的具体形式,以及T是半局部环与半完全环的充要条件。特别地,得到了左Kasch与强左Kasch n阶三角矩阵环的等价刻画。

Let T be a triangular matrix ring of order n,where n≥2 is an integer.The explicit forms of maximal ideal and minimal ideal of T,and the equivalent characterizations of T being a semi-local ring and a semi-perfect ring are given.In particular,the equivalent characterizations of left Kasch and strong left Kasch triangular matrix rings of order n are given.