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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The coordinatization of Arguesian lattices


Authors: Alan Day and Douglas Pickering
Journal: Trans. Amer. Math. Soc. 278 (1983), 507-522
MSC: Primary 06C05; Secondary 51A30
MathSciNet review: 701508
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Abstract: We show that the auxiliary planar ternary ring of an $ n$-frame in an Arguesian lattice, $ n \geqslant 3$, is indeed an associative ring with unit. The addition of two weak necessary conditions allows us to coordinatize a hyperplane of this $ n$-frame. This generalizes the classical work of von Neumann, Baer-Inaba, Jónsson and Jónsson-Monk.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0701508-6
PII: S 0002-9947(1983)0701508-6
Article copyright: © Copyright 1983 American Mathematical Society