Cocentralizing Generalized Derivations On Multilinear Polynomial On Right Ideals Of Prime Rings
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AbstractLet R be a prime ring with Utumi quotient ring U and with extended centroid C, I a non-zero right ideal of R ƒ (x1… xn) a multilinear polynomial over C which is not central valued on R and G, H two generalized derivations of R. Suppose that G(ƒ (r)) ƒ (r)- ƒ (r)H(ƒ (r)) ∈ C, for all r =(r1. there exist a; b; p ∈ U and α C such that G(x)= ax + [p, x] and H(x) = bx, for all x ∈ R, and (a-b)I=(0)=(a + p- α)I;2. R satisfies s3. R satisfies s4. R satisfies s5. there exists e(a) [ƒ (x(b) char (R) = 2 and s(c) [ƒ (x
Keyword(s):
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2011 ◽
Vol 18
(spec01)
◽
pp. 955-964
◽
Keyword(s):
2011 ◽
Vol 18
(spec01)
◽
pp. 987-998
◽