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Power Values of Derivations on Multilinear Polynomials in Prime Rings
Basudeb Dhara, Sukhendu Kar, Sachhidananda Mondal

 

Abstract

Let R be a prime ring with center Z(R) and with extended centroid C, d a derivation of R and f(x 1,…,x n ) a nonzero multilinear polynomial over C, m ≥ 1 and p ≥ 1 two integers. In the present paper, we study the situations (i) ((d(f(x 1,…,x n ))) m f(x 1,…,x n )) p = 0; (ii) ((d(f(x 1,…,x n ))) m f(x 1,…,x n )) p Z(R) for all x 1,…,x n in some subsets of R.

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