关于素环与本原环

On Prime Rings and Primitive Rings

本文利用模论方法证明：环Ｒ是一个素环的充要条件是Ｒ中存在一个本质理想Ａ，Ａ是素环．关于本原环以及单环的类似定理在作者过去的文章中已被证明，本文对这些证明利用模论方法加以改进，大大简化了这些证明．

In this paper,we use the method of theory of modules to prove following theorem:a ring R is a prime ring if and only if R has an essential ideal A which is a prime ring.Similar theorems for primitive ring and simple ring have proved by our early paper. Here,we improve those proofs by modular method.