Abstract
Let R be a prime ring with a nonzero derivation d and let f (X 1,...,Xt) be a multilinear polynomial over C, the extended centroid of R. Suppose that b[d(f(x1,...,xt)), f(x1,...,xt)]n = 0 for all xi ∈ R, where 0 ≠ b ∈ R and n is a fixed positive integer. Then f(X1,..., Xt) is centrally valued on R unless char R = 2 and dimC RC = 4. We prove a more generalized version by replacing R with a left ideal.
Original language | English |
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Pages (from-to) | 719-725 |
Number of pages | 7 |
Journal | Communications in Algebra |
Volume | 33 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2005 Dec 5 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory