矩阵环的理想

Ideal of Matrix Ring

证明了 :若Mn(R)是一个单环 ,则R是单环 ;若R是一个有单位元的环 ,则Mn(R)一定是单环 并给出了主理想环I上的矩阵环Mn(I)的全部理想的形式以及上三角形矩阵环一类理想的构造方法 .

the paper proved that R is single ring if M n(R) is single ring, M n(R) is single ring if R is single ring , gave all ideal form of matrix ring M n(I) with chief ideal I and an structural method of all ideal of upper triangular matrix ring.