Local PI theory of Jordan systems
This paper is devoted to the study of Jordan systems having a
local algebra which is PI. That condition seems to be a quite natural
obstruction to the application of eater-related methods, and has been dealt
with in several particular cases in some recent works. In this paper we
give a systematic approach inspired by ideas of associative GPI theory. We
show that the set of elements of a nondegenerate Jordan system at which the
local algebra is PI (PI-elements) is an ideal, and prove an analogue of
Amitsur's theorem on primitive GPI algebras: a primitive Jordan system
having a nonzero PI local algebra has nonzero socle, equal to its ideal of
PI-elements.
Appeared in J. Algebra 216 (1999), 302--327.
F. Montaner
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