期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1985
卷号：8
DOI：10.1155/S0161171285000138
出版社：Hindawi Publishing Corporation
摘要：In a paper with a similar title Herstein has considered the structure of prime rings which contain an element a which satisfies either [a,x]n=0 or is in the center of R for each x in R. We consider the structure of rings which contain an element a which satisfies powers of certain higher commutators. The two types which we consider are (1) […[[a,x1],x2],…xm]n=0 or is in the center of R for all x1,x2,…,xm in R and (2) [a,[x1,[x2,…,[xm−1,xm]…]]]n for all x1,x2,…,xm in R. We obtain results similar to those obtained by Herstein; however, in some cases we must strengthen the hypotheses.
