Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings

de Filippis, Vincenzo

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 271-292

Abstract (VO)

Let $R$ be a prime ring of characteristic different from 2, $Q_r$ its right Martindale quotient ring and $C$ its extended centroid. Suppose that $F$, $G$ are generalized skew derivations of $R$ with the same associated automorphism $\alpha $, and $p(x_1,\ldots ,x_n)$ is a non-central polynomial over $C$ such that $$ [F(x),\alpha (y)]=G([x,y]) $$ for all $x,y \in \{p(r_1,\ldots ,r_n)\colon r_1,\ldots ,r_n \in R\}$. Then there exists $\lambda \in C$ such that $F(x)=G(x)=\lambda \alpha (x)$ for all $x\in R$.

Détail

DOI : 10.1007/s10587-016-0255-0

Classification : 16N60, 16W25
Keywords: generalized skew derivation; prime ring

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