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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Derivations with Engel conditions
on multilinear polynomials


Authors: Pjek-Hwee Lee and Tsiu-Kwen Lee
Journal: Proc. Amer. Math. Soc. 124 (1996), 2625-2629
MSC (1991): Primary 16W25; Secondary 16N60, 16R50, 16U80
MathSciNet review: 1327023
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Abstract: Let $R$ be a prime algebra over a commutative ring $K$ with unity and let $f(X_{1}, \ldots , X_{n})$ be a multilinear polynomial over $K$. Suppose that $d$ is a nonzero derivation on $R$ such that for all $r_{1}, \ldots , r_{n}$ in some nonzero ideal $I$ of $R$, $\Big [ d\big ( f(r_{1}, \ldots , r_{n})\big ), f(r_{1}, \ldots , r_{n}) \Big ]_{k} = 0$ with $k$ fixed. Then $f(X_{1}, \ldots , X_{n})$ is central--valued on $R$ except when char $R=2$ and $R$ satisfies the standard identity $s_{4}$ in 4 variables.


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Additional Information

Pjek-Hwee Lee
Affiliation: Department of Mathematics, National Taiwan University, Taipei, Taiwan
Email: phlee@math.ntu.edu.tw

Tsiu-Kwen Lee
Affiliation: Department of Mathematics, National Taiwan University, Taipei, Taiwan
Email: tklee@math.ntu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03351-5
PII: S 0002-9939(96)03351-5
Keywords: Multilinear polynomial, derivation, generalized polynomial identity
Received by editor(s): November 4, 1994
Received by editor(s) in revised form: March 1, 1995
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society