一类幂等元模J(R)可强提升的环

将Nicholson提出的幂等元强提升概念进行了推广,定义了L-环,弱L-环,使用通常环论方法研究了L-环中本原幂等元的Local性和L-环与potent环之间的关系,证明了一个环是L-环的充分必要条件是R/J(R)是Boole环,且幂等元模J(R)可强提升,同时对具有一对零同态的Morita Context环C=A VW B,关于L-性讨论了C与A,B之间的关系.

The Rings which Idempotents Lift Strongly Module J (R)

We extend the concept of idempotents lift strongly module J (R) defined by Nicholson and introduce the concepts of L-rings and weak L-rings, and study the localcity of primitive idempotent of L-rings and the relationship between L-rings and potent rings by means of the general approach of ring, show that ring R is L-rings if and only if R/J(R) is Boolean ringand idempotents lift strongly module d(R). Let C=(AV WB) be a Morita Context ring with φ and ψ both zero bimodule homorphisms, we obtaine some property relations between C and A,B with respect to L-properity.