Let R be a prime ring of characteristic different from 2, Z(R) its center, Q its right Martindale quotient ring, C its extended centroid, F a generalized skew derivation of R, L a non-central Lie ideal of R and n≥ 1 a fixed integer such that [ F(x) , y] n= [ x, F(y) ] n, for all x, y∈ L. Then there exists λ∈ C such that F(x) = λx, for any x∈ R, unless R is an order in a 4-dimensional central simple algebra. © 2021, The Managing Editors.
Power values of quadratic polynomials with generalized skew derivations on Lie ideals
V. De Filippis
2021-01-01
Abstract
Let R be a prime ring of characteristic different from 2, Z(R) its center, Q its right Martindale quotient ring, C its extended centroid, F a generalized skew derivation of R, L a non-central Lie ideal of R and n≥ 1 a fixed integer such that [ F(x) , y] n= [ x, F(y) ] n, for all x, y∈ L. Then there exists λ∈ C such that F(x) = λx, for any x∈ R, unless R is an order in a 4-dimensional central simple algebra. © 2021, The Managing Editors.File in questo prodotto:
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