Jordan Systems of Martindale-like Quotients
In this paper we introduce the notion of Jordan
system (algebra, pair or triple system) of Martindale-like
quotients with respect to a filter of ideals as that whose
elements are absorbed into the original system by ideals of the
filter, and prove that it inherits regularity conditions such as
(semi)primeness and nondegeneracy. When we consider power filters of
sturdy ideals, the notions of Jordan systems of Martindale-like
quotients and Lie algebras of quotients are related through the
Tits-Kantor-Koecher construction, and that allows us to give
constructions of the maximal systems of quotients when the
original systems are nondegenerate.
(This paper has appeared in J. Pure Appl. Alg. 194 (2004), 127--145)
E. García < egarciag@mat.ucm.es >
M. Gómez Lozano < magomez@agt.cie.uma.es >