Commutativity Theorems for Rings With Constraints on Commutators

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Authors

  • Department of Mathematics, King Abdulaziz University, P.O. Box 30356, Jeddah-21477 ,SA

Abstract

In the present paper we investigate commutativity of semiprime ring satisfying any one of the polynomial identities x∫[xn,y]yrys[vm,x] and x∫[xn,y]yr=±[ym,x]ys for all x, y in R, where m, n, r, s and t are fixed non-negative integers, and further, we establish commutativity of rings with unity under some additional constraints. Moreover, it is also shown that the above result is true for s-unital ring. Finally, we provide some counter-examples which show that the hypotheses of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings. (See [1], [2], [5], [9], [10], [12], [14].).

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Published

1999-12-01

How to Cite

Khan, M. A. (1999). Commutativity Theorems for Rings With Constraints on Commutators. The Journal of the Indian Mathematical Society, 66(1-4), 113–124. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/21963