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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Order relation in Jordan rings and a structure theorem


Authors: Santos González and Consuelo Martínez
Journal: Proc. Amer. Math. Soc. 98 (1986), 379-388
MSC: Primary 17C10; Secondary 17C20
MathSciNet review: 857926
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Abstract: It is shown that the relation $ \leqslant $ defined by $ x \leqslant y$ if and only if $ xy = {x^2}$, $ {x^2}y = x{y^2} = {x^3}$ is an order relation for a class of Jordan rings and we prove that a Jordan ring $ R$ is isomorphic to a direct product of Jordan division rings if and only if $ \leqslant $ is a partial order on $ R$ such that $ R$ is hyperatomic and orthogonally complete.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0857926-7
PII: S 0002-9939(1986)0857926-7
Keywords: Jordan ring, partial order, direct product, nonzero nilpotent element, hyperatom, orthogonally complete
Article copyright: © Copyright 1986 American Mathematical Society