Maximal Modular Inner Ideals in Jordan Systems

Abstract

We give a description of maximal-primitizers and maximal-weak primitizers of Jordan systems, and prove two conjectures that had been previously raised: maximal modular inner ideals are maximal among all inner ideals, and maximal weakly modular inner ideals are modular.

Key Words:

• Jordan system
• Primitive
• Inner ideal

Acknowledgment

Partially supported by the DGES, PB97-1069-C02-01, and PB97-1069-C02-02.