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Proceedings of the American Mathematical Society

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

 
 

 

Direct product decomposition of alternative rings


Authors: Hyo Chul Myung and Luis R. Jimenez
Journal: Proc. Amer. Math. Soc. 47 (1975), 53-60
DOI: https://doi.org/10.1090/S0002-9939-1975-0354796-3
MathSciNet review: 0354796
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Abstract | References | Additional Information

Abstract: It is shown that any alternative ring $ A$ equipped with the relation $ \leqslant $, defined by $ x \leqslant y$ if and only if $ xy = {x^2}$, is isomorphic to a direct product of alternative division rings if and only if the relation $ \leqslant $ is a partial order on $ A$ such that $ A$ is hyperatomic and orthogonally complete.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0354796-3
Keywords: Alternative ring, nilpotent element, direct product, hyperatom, orthogonal complete
Article copyright: © Copyright 1975 American Mathematical Society

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