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

cm:9532 - Communications in Mathematics, December 23, 2021, Volume 29 (2021), Issue 3 - https://doi.org/10.2478/cm-2021-0013
(ϕ, φ)-derivations on semiprime rings and Banach algebras

Authors: Bilal Ahmad Wani

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 satisfies2D(xn) = D(xn−1)φ(x) + ϕ(xn−1)D(x) + D(x)φ(xn−1) + ϕ(x)D(xn−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 additivemappings D, G : R → R satisfying the relations2D(xn) = D(xn−1)φ(x) + ϕ(xn−1)G(x) + G(x)φ(xn−1) + ϕ(x)G(xn−1),2G(xn) = G(xn−1)φ(x) + ϕ(xn−1)D(x) + D(x)φ(xn−1) + ϕ(x)D(xn−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 purelyring theoretic results to semi-simple Banach algebras.


Volume: Volume 29 (2021), Issue 3
Published on: December 23, 2021
Imported on: May 11, 2022
Keywords: [MATH]Mathematics [math]


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