.Let K be a commutative ring with unity, R be a non-commutative prime K-algebra of characteristic different from 2, U be the Utumi quotient ring of R, C be the extended centroid of R, and G and H be two non-zero generalized derivations of R. Suppose that is a non-central multilinear polynomial over K and there exists such that for all. Then one of the following holds: (1) there exist such that and for all, with; (2) is central-valued on R and there exist such that and for all, with. © 2013 © 2013 by Walter de Gruyter Berlin Boston.
Annihilating conditions on generalized derivations acting on multilinear polynomials
DE FILIPPIS, Vincenzo;SCUDO, GIOVANNI
2013-01-01
Abstract
.Let K be a commutative ring with unity, R be a non-commutative prime K-algebra of characteristic different from 2, U be the Utumi quotient ring of R, C be the extended centroid of R, and G and H be two non-zero generalized derivations of R. Suppose that is a non-central multilinear polynomial over K and there exists such that for all. Then one of the following holds: (1) there exist such that and for all, with; (2) is central-valued on R and there exist such that and for all, with. © 2013 © 2013 by Walter de Gruyter Berlin Boston.File in questo prodotto:
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