ON CENTER-LIKE ELEMENTS IN RINGS

Joe W. Fisher ； Mohamed H. Fahmy

《International Journal of Mathematics and Mathematical Sciences》 1985卷 (1985/12) Pp. 145-149

https://doi.org/10.1155/S0161171285000138

並列摘要

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,x_1],x_2],...,x_m ]^n = 0 or is in the center of R for all x_1,x_2,...,x_m in R and (2) [a,[x_1,[x_2,...,[x_(m-1), x_m]...]]]^n = 0 for all x_1,x_2,...x_m in R. We obtain results similar to those obtained by Herstein; however, in some cases we must strengthen the hypotheses. Also we consider a third type (3) (ax^m- x^n a)^k = 0 for all x in R and extend results of Herstein and Giambruno.

並列關鍵字

Prime and semiprime rings ； primitive and semiprimitive rings ； rings with involution ； commutativity theorems