A Characterization of Generalized Derivations on Prime Rings. Issue 8 (2nd August 2016)

• Record Type: Journal Article
• Authors: Alahmadi, Adel; Ali, Shakir; Khan, Abdul Nadim; Khan, Mohammad Salahuddin
• Is Part Of: Communications in algebra. Volume 44:Issue 8(2016)
• Page Start: 3201
• Page End: 3210
• Publication Date: 2016-08-02
• Subjects: Derivation -- Engel condition -- Generalized derivation -- Generalized polynomial identities (GPI) -- Prime ring; 16W25 -- 16N60 -- 16R50; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1065861
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : Let R be a noncommutative prime ring, U be the left Utumi quotient ring of R, and k, m, n, r be fixed positive integers. If there exist a generalized derivation G and a derivation g (which is independent of G ) of R such that [ G ( x m ) x n + x n g ( x m ), x r ] k = 0, for all x ∈ R, then there exists a ∈ U such that G ( x ) = ax, for all x ∈ R . As a consequence of the result in the present article, one may obtain Theorem 1 in Demir and Argaç [10 ].