The coordinatization of Arguesian lattices

Day, Alan; Pickering, Douglas

doi:10.1090/S0002-9947-1983-0701508-6

The coordinatization of Arguesian lattices
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by Alan Day and Douglas Pickering PDF

Trans. Amer. Math. Soc. 278 (1983), 507-522 Request permission

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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