(20). Center, Centroid, Extended Centroid and Quotients in Jordan Systems.
Autores: A. Fernández López, E. García y M. Gómez Lozano.
Revista: Communications in algebra. 34, 2006, 4311-4326. (JCR:154 de 186. Factor de impacto 0.268)
Abstract: In this paper we prove that the extended centroid of a nondegenerate Jordan system is isomorphic to the centroid (and to the center in the case of Jordan algebras) of its maximal Martindale-like system of quotients with respect to the filter of all essential ideals.
pal inner ideals. We also characterize when these algebras are Artinian, proving in particular that a finitary simple Lie algebra over an algebraically closed field of characteristic zero is Artinian if and only if it is finite dimensional. Because it is useful for our approach, we provide a characterization of the trace of a finite rank operator on a vector space over a division algebra which is intrinsic in the sense that it avoids imbeddings into finite matrices.