关于根与底座的几点注记

Some remarks on the radical and socle

根与底座是环论中的重要概念之一,在代数表示理论等方面也有着重要的应用。介绍了根与底座的几种等价定义,证明了各个定义的相互等价性,并且研究了广义矩阵环的Jacobson根。

Radical and socle are some of the most important concepts in ring theory, they also have important applications in algebra represent theory. In this paper, some equivalent definitions of the radical and socle are given, the Jacobson radical of generalized matrix ring is studied.