Nil polynomials of prime rings

[摘要] Assume that R is a prime ring without nonzero nil one-sided ideals and that f(x(1),...,x(d)) is a polynomial in the noncommuting variables x(1),...,x(d) and with the coefficients in the extended centroid C of R. If for all r(1),...,r(d) is an element of R, there exists an integer n = n(r(1),...,r(d)) greater than or equal to 1, depending on r(1),..., r(d) is an element of R, such that f(r(1),...,r(d))(n) = 0, then either f(r(1),...,r(d)) = 0 for all r(1),...,r(d) is an element of R or R is a finite matrix ring over a finite field. (C) 1996 Academic Press, Inc.

[发布日期] 1996-12-15