semiprimitive ring

When ring R , as an R module, is YJ injective, this paper gives some equivalent conditions among nonsingular ring, semiprimitive ring, pp ring and regular rings.

利用非奇异环、半本原环、pp环刻画正则环 ,当 R是 YJ内射 R模时 ,给出以上环的等价的几个条件 ,同时给出强正则环及半单环的刻画 。

Density of primitive semiring and Kaplansky s theorem;

本原半环的稠密性及Kaplansky定理

In this paper a whole new describition is given about Jsemisimple semirings through semiprimitive semirings.

利用半本原半环给出了J 半单半环的一个新刻画。

(2)Let R be a primitive ring,M be a faithful and non-reduce left R -module and M= Rm(o≠or∈M),then L={r∈R|rm=0} is an essential left ideal of R if and only if R is not a ring with maximal annihilator left ideal.

(2)设 R 是本原环,M 是忠实既约 R-模,M=Rm(0≠m∈M),则 L={r∈R|rm=0}是 R 的本质左理想子环的必要充分条件是 R 不含极大零化左理想。

In this paper, we describes a group as a primitive ring by means of that ring R is a primitive ring if and only if there exists irreducible faithful module over R , through decomposing irreducible module over RG into irreducible module over RH and extending module over RH into irreducible module over RG .

借助于环 R为本原环的充要条件是存在忠实既约模 ,通过将既约 RG-模分解为既约 RH-模及将既约 RH-模扩张为既约 RG-模 ,刻画了群环为本原