COMMUTATIVlTY THEOREMS FOR RINGS WITH CONSTRAINTS ON COMMUTATORS
نویسنده
چکیده
In this paper, we generalize sone well-known commutativity theorems for associative rings as follows: Let ’, > 1. ,,, .,, and be fixed nou-ncgative integers such that s ik m1, or i/= n1, and let R be a ring xvith unity satisfying the polynomial identity y*[x’,y] [x,y’]x for all y R. Sul,lose that (i) R has Q(z) (that is n[x,y] 0 implies [z,y] 0); (ii) the set of d] nilpotent ,,lem,’nts of R is central for > 0, and (iii) the set of all zero-divisors of R is also central hr > 0. Then R is commutative. If Q(n) is replaced by "rn and n are relatively prime pobitive integers," then R is commutative if extra constraint is given. Other related commutativity results are also obtained.
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تاریخ انتشار 2004