Goldie theory for Jordan algebras
It is shown that Zelmanov's version
of Goldie's conditions still characterize quadratic algebras having an
artinian algebra of quotients which is nondegenerate. At the same
time, Jordan versions of the main notions of the
associative theory are studied. In particular, it is proved
that the nondegenerate Jordan
algebras of finite capacity are precisely the algebras of quotients
of nondegenerate Jordan algebras having the property
that an inner ideal is
essential if and only if it contains a regular element.
(This paper has appeared in J. Algebra 248 (2002), no. 2, 397--471)
Antonio Fernandez Lopez <emalfer@ccuma.sci.uma.es>
Eulalia Garcia Rus <garcia@agt.cie.uma.es>
Fernando Montaner <fmontane@posta.unizar.es>