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GENERALIZED SKEW DERIVATIONS AS JORDAN HOMOMORPHISMS ON MULTILINEAR POLYNOMIALS

Vincenzo De Filippis
대한수학회 (The Korean Mathematical Society)|2015.01|대한수학회지 (Journal of the KMS)|제52권 제1호|pp. 191-207

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참고문헌

키워드

prime ringgeneralized skew derivationpolynomial identity
주제분류수학

초록

Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended cen- troid. Suppose that G is a nonzero generalized skew derivation of R, is the associated automorphism of G, f(x1, . . . , xn) is a non-central multilinear polynomial over C with n non-commuting variables and S = {f(r1, . . . , rn) | r1, . . . , rn ∈ R}. If G acts as a Jordan homomorphism on S, then either G(x) = x for all x ∈ R, or G = α.

Abstract

Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended cen- troid. Suppose that G is a nonzero generalized skew derivation of R, is the associated automorphism of G, f(x1, . . . , xn) is a non-central multilinear polynomial over C with n non-commuting variables and S = {f(r1, . . . , rn) | r1, . . . , rn ∈ R}. If G acts as a Jordan homomorphism on S, then either G(x) = x for all x ∈ R, or G = α.

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