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Acta Mathematica Vietnamica

Power Values of Derivations on Multilinear Polynomials in Prime Rings

icon-email 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(x1,,xn) a nonzero multilinear polynomial over C, m1 and p1 two integers. In the present paper, we study the situations (i) ((d(f(x1,,xn)))mf(x1,,xn))p=0; (ii) ((d(f(x1,,xn)))mf(x1,,xn))pZ(R) for all x1,,xn in some subsets of R.