Let R be a prime ring, f(X-1, ..., X-n) a multilinear polynomial which is not central-valued on R, and G a nonzero generalized skew derivation of R. Suppose that G(f(x(1), ..., x(n))) is zero or invertible for all x(1), ..., x(n) is an element of R. Then it is proved that R is either a division ring or the ring of all 2 x 2 matrices over a division ring. This result simultaneously generalizes a number of results in the literature.
Generalized Skew Derivations With Invertible Values On Multilinear Polynomials
DE FILIPPIS, Vincenzo
2012-01-01
Abstract
Let R be a prime ring, f(X-1, ..., X-n) a multilinear polynomial which is not central-valued on R, and G a nonzero generalized skew derivation of R. Suppose that G(f(x(1), ..., x(n))) is zero or invertible for all x(1), ..., x(n) is an element of R. Then it is proved that R is either a division ring or the ring of all 2 x 2 matrices over a division ring. This result simultaneously generalizes a number of results in the literature.File in questo prodotto:
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