Let R be a prime ring of characteristic different from 2, Qr its right Martindale quotient ring, F and G two non-zero generalized skew derivations of R, associated with the same automorphism α and commuting with α. In this work we describe all possible forms of F and G in the following two cases: (a) there exist a, b∈ Qr and a non-central Lie ideal L of R such that aF(x) b= 0, for all x∈ L ; (b) there exist a1, a2, b1, b2∈ Qr such that a1F(x) b1+ a2G(x) b2= 0, for all x∈ R.
Two Remarks on Generalized Skew Derivations in Prime Rings
De Filippis V.
;Rania F.
2022-01-01
Abstract
Let R be a prime ring of characteristic different from 2, Qr its right Martindale quotient ring, F and G two non-zero generalized skew derivations of R, associated with the same automorphism α and commuting with α. In this work we describe all possible forms of F and G in the following two cases: (a) there exist a, b∈ Qr and a non-central Lie ideal L of R such that aF(x) b= 0, for all x∈ L ; (b) there exist a1, a2, b1, b2∈ Qr such that a1F(x) b1+ a2G(x) b2= 0, for all x∈ R.File in questo prodotto:
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