Order relation in Jordan rings and a structure theorem

González, Santos; Martínez, Consuelo

doi:10.1090/S0002-9939-1986-0857926-7

Order relation in Jordan rings and a structure theorem
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by Santos González and Consuelo Martínez PDF

Proc. Amer. Math. Soc. 98 (1986), 379-388 Request permission

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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