Two notes on the axiomatics of structures with parallelism

Authors

  • Victor Pambuccian

DOI:

https://doi.org/10.1285/i15900932v20n2p93

Keywords:

Central translation structure, Translation plane, Affine ring-geometry, Integral domains with a right GCD

Abstract

We provide: (1) an independent quantifier-free axiomatization for André's central translation structures and state a conjecture, which, if true, would show a very strong connection between central translation structures and translation planes; (2) a first-order axiomatization of Everett’s and Permutti’s affine geometries over rings without zero divisors in which any two non-zero elements have a right greatest common divisor.

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Published

31-12-2001

Issue

Volume 20, Issue 2 (2000-2001)

Section

Articoli

License

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Gli autori che pubblicano in questa rivista accettano i termini e le condizioni specificate nella licenza Creative Commons di cui al link sottostante.

http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode