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Generalized derivations in prime rings and noncommutative Banach algebras

Vincenzo De Filippis
대한수학회 (The Korean Mathematical Society)|2008.11|대한수학회보 (Bulletin of the KMS)|제45권 제4호|pp. 621-629

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참고문헌

키워드

derivationsBanach algebrasprime ringdifferential identities
주제분류수학

초록

Let R be a prime ring of characteristic different from 2, C the extended centroid of R, and δ a generalized derivations of R. If [[δ(x), x], δ(x)] = 0 for all x ∈ R then either R is commutative or δ(x) = ax for all x ∈ R and some a ∈ C. We also obtain some related result in case R is a Banach algebra and δ is either continuous or spectrally bounded.

Abstract

Let R be a prime ring of characteristic different from 2, C the extended centroid of R, and δ a generalized derivations of R. If [[δ(x), x], δ(x)] = 0 for all x ∈ R then either R is commutative or δ(x) = ax for all x ∈ R and some a ∈ C. We also obtain some related result in case R is a Banach algebra and δ is either continuous or spectrally bounded.

참고문헌 (23)

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