On generalized derivations in rings and Banach algebras
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Let R be a ring, P a prime ideal, F1, F2 are generalized derivations of R and H1, H2 two multipliers. The purpose of this paper is to classify the involved mappings satisfying the following differential identity: F1(x) ⊥ F2(y) - H1(x) ⊥ H2(y) ∈ P for all x, y ∈ R, where ⊥ represents either the usual product, or the Lie product [.,.], or the Jordan product ∘. Furthermore, as an application, the same identities are studied locally on nonvoid open subsets of prime Banach algebras.
Abstract
Let R be a ring, P a prime ideal, F1, F2 are generalized derivations of R and H1, H2 two multipliers. The purpose of this paper is to classify the involved mappings satisfying the following differential identity: F1(x) ⊥ F2(y) - H1(x) ⊥ H2(y) ∈ P for all x, y ∈ R, where ⊥ represents either the usual product, or the Lie product [.,.], or the Jordan product ∘. Furthermore, as an application, the same identities are studied locally on nonvoid open subsets of prime Banach algebras.
참고문헌 (11)
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