Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Order relation in quadratic Jordan rings and a structure theorem

Authors: Santos González and Consuelo Martínez
Journal: Proc. Amer. Math. Soc. 104 (1988), 51-54
MSC: Primary 17C10
MathSciNet review: 958042
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the relation defined by $ x \leq y$ if and only if $ {V_x}x = {V_x}y$ and $ {U_x}x = {U_x}y = {U_y}x$ is an order relation for quadratic Jordan algebras without nilpotent elements, which extends our previous one for linear Jordan algebras, and reduces to the usual Abian order for associative algebras. We prove that a quadratic Jordan algebra is isomorphic to a direct product of division algebras if and only if the algebra has no nilpotent elements and is hyperatomic and orthogonally complete.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17C10

Retrieve articles in all journals with MSC: 17C10

Additional Information

Keywords: Quadratic Jordan algebras, partial order, direct product, nilpotent element, hyperatomic, orthogonally complete
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society