Local PI theory of Jordan systems II
This paper continues a previous study of Jordan systems having
nonzero PI-elements, that is elements at which the local algebra is PI. We
prove an analogue of Martindale's theorem on prime associative algebras
with a generalized identity. To do that, we first introduce the extended
centroid of a nondegenerate Jordan system, and define the scalar extension
naturally attached to it, which we call the extended central closure. The
main theorem of the paper asserts that a strongly prime Jordan system with
a nonzero PI-element has a primitive extended central closure which has
therefore nonzero socle.
F. Montaner <fmontane@posta.unizar.es>