Generalized derivations on Jordan ideals in prime rings | Zendy

Mahmmoud EL-SOUFI | Zendy; Ahmed Aboubakr | Zendy

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Generalized derivations on Jordan ideals in prime rings

Author(s) -

Mahmmoud EL-SOUFI,

Ahmed Aboubakr

Publication year - 2014

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1211-42

Subject(s) - subring , mathematics , center (category theory) , prime (order theory) , semiprime ring , prime ring , combinatorics , torsion (gastropod) , ideal (ethics) , ring (chemistry) , pure mathematics , crystallography , law , medicine , chemistry , surgery , organic chemistry , political science

Let R be a 2-torsion free prime ring with center Z(R), J be a nonzero Jordan ideal also a subring of R, and F be a generalized derivation with associated derivation d. In the present paper, we shall show that JZ(R) if any one of the following properties holds: (i) (F(u);u) 2 Z(R), (ii) F(u)u = ud(u), (iii) d(u 2 ) = 2F(u)u, (iv) F(u 2 ) 2uF(u) = d(u 2 ) 2ud(u), (v) F 2 (u) + 3d 2 (u) = 2Fd(u) + 2dF(u), (vi) F(u 2 ) = 2uF(u) for all u 2 J.

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