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Juan José Martinez 《代数通讯》2013,41(3):719-732
ABSTRACT Let R be a prime ring with a nonzero derivation d and let f(X 1,…,X t ) be a multilinear polynomial over C, the extended centroid of R. Suppose that b[d(f(x 1,…,x t )), f(x 1,…,x t )] n = 0 for all x i ∈ R, where 0 ≠ b ∈ R and n is a fixed positive integer. Then f(X 1,…,X t ) is centrally valued on R unless char R = 2 and dim C RC = 4. We prove a more generalized version by replacing R with a left ideal. 相似文献
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