The coordinatization of Arguesian lattices-Reference-Cited by-同舟云学术

The coordinatization of Arguesian lattices

Published:1983 Issue:2 Volume:278 Page:507-522
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Day Alan,Pickering Douglas

Abstract

We show that the auxiliary planar ternary ring of an n n -frame in an Arguesian lattice, n ⩾ 3 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 n -frame. This generalizes the classical work of von Neumann, Baer-Inaba, Jónsson and Jónsson-Monk.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1983-278-02/S0002-9947-1983-0701508-6/S0002-9947-1983-0701508-6.pdf

Reference18 articles.

1. On coordinates in modular lattices with a homogeneous basis;Artmann, Benno;Illinois J. Math.,1968

2. A unified theory of projective spaces and finite abelian groups;Baer, Reinhold;Trans. Amer. Math. Soc.,1942

3. P. Crawley and R. Dilworth, Algebraic theory of lattices, Prentice-Hall, Englewood Cliffs, N. J., 1973.

4. Complemented modular lattices and projective spaces of infinite dimension;Frink, Orrin, Jr.;Trans. Amer. Math. Soc.,1946

5. The amalgamation property in equational classes of modular lattices;Grätzer, G.;Pacific J. Math.,1973

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