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Article Dans Une Revue Communications in Mathematics Année : 2021

(ϕ, φ)-derivations on semiprime rings and Banach algebras

Résumé

Let R be a semiprime ring with unity e and φ, ϕ be automorphisms of R. In this paper it is shown that if R satisfies 2D(x n ) = D(x n−1 )φ(x) + ϕ(x n−1 )D(x) + D(x)φ(x n−1 ) + ϕ(x)D(x n−1 ) for all x ∈ R and some fixed integer n ≥ 2, then D is an (φ, ϕ)-derivation. Moreover, this result makes it possible to prove that if R admits an additive mappings D, G : R → R satisfying the relations 2D(x n ) = D(x n−1 )φ(x) + ϕ(x n−1 )G(x) + G(x)φ(x n−1 ) + ϕ(x)G(x n−1 ), 2G(x n ) = G(x n−1 )φ(x) + ϕ(x n−1 )D(x) + D(x)φ(x n−1 ) + ϕ(x)D(x n−1 ), for all x ∈ R and some fixed integer n ≥ 2, then D and G are (φ, ϕ)- -derivations under some torsion restriction. Finally, we apply these purely ring theoretic results to semi-simple Banach algebras.
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hal-03665003 , version 1 (11-05-2022)

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Bilal Ahmad Wani. (ϕ, φ)-derivations on semiprime rings and Banach algebras. Communications in Mathematics, 2021, Volume 29 (2021), Issue 3 (3), pp.371 - 383. ⟨10.2478/cm-2021-0013⟩. ⟨hal-03665003⟩

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