Author:
Abu-Khuzam Hazar,Bell Howard,Yaqub Adil
Abstract
It is shown that an n-torsion-free ring R with identity such that, for all x, y in R, xnyn = ynyn and (xy)n+1 − xn+1yn+1 is central, must be commutative. It is also shown that a periodic n–torsion-free ring (not necessarily with identity) for which (xy)n − (yx)n is always in the centre is commutative provided that the nilpotents of R form a commutative set. Further, examples are given which show that all the hypotheses of both theorems are essential.
Publisher
Cambridge University Press (CUP)
Reference11 articles.
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