Almost Jordan Generalized Derivations in Prime Rings

Dr. D. Bharathi; V. Ganesh

doi:https://doi.org/10.14445/22315373/IJMTT-V18P503

International Journal of Mathematics Trends and Technology

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Volume 18 | Number 1 | Year 2015 | Article Id. IJMTT-V18P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V18P503

Almost Jordan Generalized Derivations in Prime Rings

Dr. D. Bharathi, V. Ganesh

Abstract

Let R be a prime ring with char≠ 2, D(. , . ) be a symmetric bi-derivation of R, 0≠ d be trace of D (. , .) , f –(α , β )r – d be right almost Jordan generalized derivation of R, β is surjective and a ∈ R. If af(x) = 0 for all x ∈R, then a = 0 and let R be a prime ring with char R ≠ 2,3 , D (. , . , .) be permuting tri-derivation of R , 0 ≠ d be the trace of D (. , . , .). ( f– d )r be right almost Jordan generalized derivations of R. If [ f(x) , r ] = 0 for all x , r Ε R, then R is commutative ring.

Keywords

Ring , Prime ring, derivation, Jordan derivation, Generalized derivation, Jordan generalized derivation, Symmetric bi-derivation, Permuting tri-derivation, Almost Jordan generalized derivation.

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Citation :

Dr. D. Bharathi, V. Ganesh, "Almost Jordan Generalized Derivations in Prime Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 18, no. 1, pp. 14-20, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V18P503