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A THEOREM ON DERIVATIONS ON PRIME RINGS

Part of: Rings and algebras with additional structure Rings with polynomial identity

Published online by Cambridge University Press:  18 November 2011

KUN-SHAN LIU
KUN-SHAN LIU*
Affiliation:
Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (email: [email protected])
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Abstract

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Let R be a prime ring, let I be a nonzero ideal of R and let n be a fixed positive integer. We prove that if the characteristic of R is either 0 or a prime p that is greater than 2n, then an additive map d that satisfies d(xn+1)=∑ nj=0xn−jd(x)xj for all x∈I must be a derivation.

Keywords

prime ringderivationsadditive mapgeneralized polynomial identityfunctional identity

MSC classification

Secondary: 16W25: Derivations, actions of Lie algebras 16R20: Semiprime p.i. rings, rings embeddable in matrices over commutative rings 16R60: Functional identities
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 2 , October 2011 , pp. 219 - 229
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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