摘要
笔者在文献[1]中讨论了双群结合环的构造。本文进一步研究双群结合环的幂零性,并得到了类似于环论中的结果及每一个强诣零理想可表为某些幂零理想之和;最后讨论了在某些链条件下的幂零性,把环论中著名的Hopkins 定理与 Levitzki 定理推广到双群结合环。
The structure of two-group associative rings is discussed in (1);herein, the nilpotency of these rings is studied.The results obtained are analogical to the theories of rings,and it is shown that any strong nil ideal can be expressed as the sum of some nilpotent ideals.Finally,the nilpotency of two-group associative rings under certain chain conditions is studied by extending the classical Hopkins theorem and Levitzki theorem to these rings.
