Let R be a noncommutative prime ring of characteristic different from 2 and 3, C the extended centroid of R, F and G two generalized derivations of R, d a nonzero derivation of R and f(x1, … , xn) a multilinear polynomial over C. Suppose that I is a nonzero ideal of R and f(I) = { f(x1, … , xn) | x1, … , xn∈ I}. If f(x1, … , xn) is not central valued on R and d(F2(u)u-G(u2))=0for all u∈ f(I) , then all possible forms of the maps F, G and d are described in the present paper. © 2021, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.
Vanishing Derivations on Some Subsets in Prime Rings Involving Generalized Derivations
De Filippis V.;
2021-01-01
Abstract
Let R be a noncommutative prime ring of characteristic different from 2 and 3, C the extended centroid of R, F and G two generalized derivations of R, d a nonzero derivation of R and f(x1, … , xn) a multilinear polynomial over C. Suppose that I is a nonzero ideal of R and f(I) = { f(x1, … , xn) | x1, … , xn∈ I}. If f(x1, … , xn) is not central valued on R and d(F2(u)u-G(u2))=0for all u∈ f(I) , then all possible forms of the maps F, G and d are described in the present paper. © 2021, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.File in questo prodotto:
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