Derivations cocentralizing polynomials
Journal
Taiwanese Journal of Mathematics
Journal Volume
2
Journal Issue
4
Pages
457-467
Date Issued
1998
Author(s)
Shiue, W.-K.
Abstract
Let R be a prime ring with extended centroid C and f(X1 , . . . , Xt) a polynomial over C which is not central-valued on RC. Suppose that d and δ are two derivations of R such that d(f(x1 , . . . , xt))f(x1 , . . . , xt) - f(x1 , . . . ,xt)δ(f(x1 , . . . , xt)) ∈ C for all x1 , . . . , xt in R. Then either d = 0 = δ, or δ = -d and f(X1 , . . . , Xt)2 is central-valued on RC, except when char R = 2 and dimc RC = 4.
Type
journal article