Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid. In this paper we define b-generalized skew derivations of prime rings. Then we describe all possible forms of two b-generalized skew derivations F and G satisfying the condition F(x)x − xG(x) = 0, for all x ∈ S, where S is the set of the evaluations of a multilinear polynomial f(x1, …, xn) over C with n non-commuting variables. Several potential research topics related to our current work are also presented. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings
De Filippis V.
;Scudo G.;
2021-01-01
Abstract
Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid. In this paper we define b-generalized skew derivations of prime rings. Then we describe all possible forms of two b-generalized skew derivations F and G satisfying the condition F(x)x − xG(x) = 0, for all x ∈ S, where S is the set of the evaluations of a multilinear polynomial f(x1, …, xn) over C with n non-commuting variables. Several potential research topics related to our current work are also presented. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.File in questo prodotto:
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