Ler R be a non-commutative prime ring with extended centroid C, I a non-zero left ideal of R and F a non-zero generalized derivation of R. If F satisfies an Engel-type condition on the powers of the element of I, then F(x)=xa for all x in R, with Ia=Ic for suitable c in C. In particular F(x)=cx for all x in I.
Generalized derivations with engel conditions on one-sided ideals
DE FILIPPIS, Vincenzo
2008-01-01
Abstract
Ler R be a non-commutative prime ring with extended centroid C, I a non-zero left ideal of R and F a non-zero generalized derivation of R. If F satisfies an Engel-type condition on the powers of the element of I, then F(x)=xa for all x in R, with Ia=Ic for suitable c in C. In particular F(x)=cx for all x in I.File in questo prodotto:
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