On Lie ideals and $ (\sigma, \tau) $-Jordan derivations on prime rings | Zendy

Mohammad Ashraf | Zendy; Murtaza A. Quadri | Zendy; Nadeem ur Rehman | Zendy

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On Lie ideals and $ (\sigma, \tau) $-Jordan derivations on prime rings

Author(s) -

Mohammad Ashraf,

Murtaza A. Quadri,

Nadeem ur Rehman

Publication year - 2001

Publication title -

tamkang journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 18

eISSN - 0049-2930

pISSN - 2073-9826

DOI - 10.5556/j.tkjm.32.2001.338

Subject(s) - mathematics , automorphism , prime (order theory) , sigma , ideal (ethics) , prime ring , combinatorics , ring (chemistry) , pure mathematics , physics , chemistry , philosophy , epistemology , quantum mechanics , organic chemistry

Let $ R $ be a prime ring with characteristic different from two and let $ U $ be a Lie ideal of $ R $ such that $ u^2 in U $ for all $ u in U $. Suppose that $ sigma, au $ are automorphisms of $ R $. In the present paper, it is shown that if $ d $ is an additive mapping of $ R $ into itself satisfying $ d (u^2) = d(u) sigma (v) + au (u) d(v) $ for all $ u,v in U $, then $ d(uv) = d(u) sigma (v) + au(u) d(v) $ for all $ u, v in U $.

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