Higher – Derivations in Completely Semi Prime -Rings

M.M. Rahman¹ and S.K. Paul^2,*
¹Department of Mathematics, Jagannath University, Dhaka, Bangladesh.
^2,*Department of Basic Sciences and Humanities, University of Asia Pacific, Dhaka, Bangladesh.

*e-mail: sanjitkpaul@gmail.com

The aim of the present paper is to prove d_n (uαm) = Ʃ_i+j=n d_i(u)αd_j(m), ∀u ∈ U, m∈M, α ∈ Γ, n ∈ N, where  is a 2-torsion free completely semi prime  Γ-ring satisfying the condition aαbβc = aβbαc, ∀ a,b,c ∈ M and α,β∈ Γ,U is an admissible Lie ideal of M and D = (d_i)_i∈N is a higher (U,M)-derivation of M.

Keywords: Admissible Lie ideal, higher -derivation, completely semiprime -ring.

2010 AMS Subject Classification: Primary 13N15; Secondary 16W10, 17C50.

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