Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 2, pp. 333-338 (2002)
On a Certain Functional Identity in Prime Rings, II
M. Bresar, M. A. Chebotar
Department of Mathematics, PF, University of Maribor, Maribor, Slovenia, e-mail: bresar@uni-mb.si; Department of Mechanics and Mathematics, Tula State University, Tula, Russia, e-mail: mchebotar@tula.net
Abstract: Let $\cal R$ be a prime ring. It is shown that, under certain restrictions on char$({\calR})$, $\cal R$ admits a functional identity $f(x)xf(x)\ldots xf(x)=0$, $x\in {\cal R}$, where $f:{\cal R}\to {\cal R}$ is a nonzero additive map, if and only if its central closure $\cal S$ contains an idempotent $e\neq 0,1$ such that $e{\cal S} e = {\cal C} e$ where $\cal C$ is the extended centroid of $\cal R$.
Classification (MSC2000): 16W10,16W25,16R50
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