GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS

Authors : E. ALBAŞ, N. ARGAÇ, V. De FİLİPPİS, Ç. DEMİR

Pages : 69-83

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Publication Date : 2014-01-01

Article Type : Other Papers

Abstract :Let R be a prime ring, f insert ignore into journalissuearticles values(x, . . . , xn ); a multilinear polynomial over Cin n noncommuting indeterminates, I a nonzero right ideal of R, andF : R → R be a nonzero generalized skew derivation of R.Suppose that F insert ignore into journalissuearticles values(f insert ignore into journalissuearticles values(r, . . . , rn ););f insert ignore into journalissuearticles values(r, . . . , rn ); ∈ C, for all r, . . . , rn ∈ I.If f insert ignore into journalissuearticles values(x, . . . , xn ); is not central valued on R, then either charinsert ignore into journalissuearticles values(R); = 2and R satisfies sor one of the following holds:insert ignore into journalissuearticles values(i ); f insert ignore into journalissuearticles values(x, . . . , xn );x n+1 is an identity for I;insert ignore into journalissuearticles values(ii ); F insert ignore into journalissuearticles values(I);I = insert ignore into journalissuearticles values(0);;insert ignore into journalissuearticles values(iii ); [f insert ignore into journalissuearticles values(x, . . . , xn );, x n+1 ]x n+2 is an identity for I, there existb, c, q ∈ Q with q an invertible element such that F insert ignore into journalissuearticles values(x); =bx − qxq−1 c for all x ∈ R, and q−1 cI ⊆ I.Moreover, inthis case either insert ignore into journalissuearticles values(b − c);I = insert ignore into journalissuearticles values(0); or b − c ∈ C and f insert ignore into journalissuearticles values(x, . . . , xn ); is central valued on R.
Keywords : Identity, generalized skew derivation, automorphism, semi, prime ring