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Posner's second theorem, multilinear polynomials and vanishing derivations

Part of: Radicals and radical properties of rings Rings and algebras with additional structure

Published online by Cambridge University Press:  09 April 2009

Vincenzo De Filippis  and
Onofrio Mario Di Vincenzo
Vincenzo De Filippis
Affiliation:
Dipartimento di Matematica, Università di Messina, Salita Sperone 31, 98166 Messina, Italia e-mail: [email protected]
Onofrio Mario Di Vincenzo
Affiliation:
Dipartimento di Matematica, Universitá di Bari, Via Orabona 4, 70125 Bari, Italia e-mail: [email protected]
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Abstract

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Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, d and δ non-zero derivations of R, f (x1,…, xn) a multilinear polynomial over K.If

then f(x1,…,xnis central-valued on R.

Keywords

derivationPIGPIprime ringdifferential identity

MSC classification

Secondary: 16N60: Prime and semiprime rings 16W25: Derivations, actions of Lie algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 3 , June 2004 , pp. 357 - 368
Copyright
Copyright © Australian Mathematical Society 2004

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