IJPAM: Volume 20, No. 2 (2005)

MULTILINEAR POLYNOMIALS AND POWER
VALUES OF DERIVATIONS ON RIGHT IDEALS

Vincenzo De Filippis
Department of Mathematics
University of Messina
Salita Sperone 31, Messina, 98166, ITALY
e-mail: enzo@dipmat.unime.it


Abstract.Let $K$ be a commutative ring with unity, $R$ a prime K-algebra, with extended centroid $C$, $d$ a non-zero derivation of $R$, $f(x_1, \dots ,x_n)$ a multilinear polynomial over $K$, $I$ a non-zero right ideal of $R$, $a\in R$ and $m\geq 1$ a fixed integer. If $a(d(f(r_1, \dots ,r_n)-f(r_1, \dots ,r_n))^m$
$=0$, for all $r_1, \dots ,r_n \in I$, then one of the following holds: (i) $f(x_1, \dots $,
$x_n)x_{n+1}$ is an identity for $I$; (ii) $aI=ad(I)=0$.

Received: March 9, 2005

AMS Subject Classification: 16N60, 16W25

Key Words and Phrases: derivation, PI, GPI, prime ring, differential identity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 2