2010•Dirāsāt. Al-ʿulūm al-asāsiyyaẗRequires access
(σ, τ)– Derivations on Jordan Ideals
A. H. Majeed, Asawer D. Hamdi
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Abstract
Let R be a 2-torsion-free prime ring , J a nonzero Jordan ideal and a subring of R. For a (σ,σ)–derivation d: R→R, we prove the following results: (1) If F is a generalized (σ,σ)–derivation which acts as a homomorphism or as an anti-homomorphism on J, then either d = 0 on R or ⊆ Z(R). (2) If d is a (σ,τ)–derivation which acts as a homomorphism on J, then d = 0 on R or ⊆ Z (R).