Derivations with engel conditions on multilinear polynomials
Journal
Proceedings of the American Mathematical Society
Journal Volume
124
Journal Issue
9
Pages
2625-2629
Date Issued
1996
Author(s)
Lee, P.-H.
Abstract
Let R be a prime algebra over a commutative ring K with unity and let f(X1, . . . , Xn) be a multilinear polynomial over K. Suppose that d is a nonzero derivation on R such that for all r1, . . . , rn in some nonzero ideal I of R, [d(f(r1, . . . , rn)), f(r1, . . . , rn)]k = 0 with k fixed. Then f(X1, . . . , Xn) is central-valued on R except when char R = 2 and R satisfies the standard identity 54 in 4 variables. © 1996 American Mathematical Society.
Type
journal article