Abstract
Assume thatRis a prime ring without nonzero nil one-sided ideals and thatf(x1,…,xd) is a polynomial in the noncommuting variablesx1,…,xdand with the coefficients in the extended centroidCofR. If for allr1,…,rd∈R, there exists an integern=n(r1,…,rd)≥1, depending onr1,…,rd∈R, such thatf(r1,…,rd)n=0, then eitherf(r1,…,rd)=0 for allr1,…,rd∈RorRis a finite matrix ring over a finite field.
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