关于素环的几个定理

Some Theorems On Prime Rings

本文给出了判断本原环，有单位元的单环和除环的充分必要条件，主要结果见定理１—７。

In this paper the main results are following theorems: (1)A prime ring is a primitre ring, asimple ring with unit or a division ring, respectively, if and only if there exists its ideal which is aprimitre ring, a sinple ring with unit or a division ring. (2)The result is still true when we replaceprime ring by ring and ideal by essential ideal in (1). (3) A prime ring is a subdirectly irreduciblering if and only if there exists its ideal which is a simple ring.