Let R be a prime ring of characteristic different from 2, Q its right Martindale quotient ring, C its extended centroid, I a right ideal of R, a ∈ Q, G a nonzero X-generalized skew derivation of R, f (x1, . . . , xn) a multilinear polynomial over C with n non-commuting variables, and S the set of the evaluations of f (x1, . . . , xn) on I. If [ f (x1, . . . , xn), xn+1]xn+2 is not an identity for I and aG(x)x ∈ Z(R) for all x ∈ S, then we determine all the possible forms of G.
Central Values of X-generalized Skew Derivations on Right Ideals in Prime Rings
Luisa, Carini;Vincenzo, De Filippis
2022-01-01
Abstract
Let R be a prime ring of characteristic different from 2, Q its right Martindale quotient ring, C its extended centroid, I a right ideal of R, a ∈ Q, G a nonzero X-generalized skew derivation of R, f (x1, . . . , xn) a multilinear polynomial over C with n non-commuting variables, and S the set of the evaluations of f (x1, . . . , xn) on I. If [ f (x1, . . . , xn), xn+1]xn+2 is not an identity for I and aG(x)x ∈ Z(R) for all x ∈ S, then we determine all the possible forms of G.File in questo prodotto:
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