Let K be a commutative ring with unity, R a prime K-algebra, f(x_i) a multilinear polynomial over K, d and g non-zero derivations of R. If [d(f(x_i)),g(f(x_i))] is central valued for all x_i in R, then either f(x_i) is central valued on R, or d and g are linearly dependent over the extended centroid of R, except when the characteristic of R is 2 and R satisfies the standard identity of degree 4.
QUADRATIC CENTRAL DIFFERENTIAL IDENTITIES ON A MULTILINEAR POLYNOMIAL
DE FILIPPIS, Vincenzo;
2008-01-01
Abstract
Let K be a commutative ring with unity, R a prime K-algebra, f(x_i) a multilinear polynomial over K, d and g non-zero derivations of R. If [d(f(x_i)),g(f(x_i))] is central valued for all x_i in R, then either f(x_i) is central valued on R, or d and g are linearly dependent over the extended centroid of R, except when the characteristic of R is 2 and R satisfies the standard identity of degree 4.File in questo prodotto:
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