满足(幂零元)左-Zorn链条件的环

Rings satisfying the condition for(nilpotent element) left zorn chain

通过引进(幂零元)左zorn链条件,弱Her-(单侧)理想,K-商环等概念,讨论Her-环的性质,得到一系列结果.并给出环上Kothe猜测成立的一个充要条件,由此给出环上Herstein猜测成立的一个充要条件.

In this paper, we introduce (nilpotent element) left (right) zorn chain condition, Kothe\|quotient rings, and so on study properties of Her\|rings and obtain a series of important results. On the other hand, we give a sufficient and necessary condition of Kothe conjecture and Herstein conjecture.\;