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Commutativity Theorems for Rings With Constraints on Commutators


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1 Department of Mathematics, King Abdulaziz University, P.O. Box 30356, Jeddah-21477, Saudi Arabia
     

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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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  • Commutativity Theorems for Rings With Constraints on Commutators

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Authors

Moharram A. Khan
Department of Mathematics, King Abdulaziz University, P.O. Box 30356, Jeddah-21477, Saudi Arabia

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].).