Two notes on the axiomatics of structures with parallelism

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2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)93-104
Number of pages12
JournalNote di Matematica
Issue number2
StatePublished - Dec 1 2001


  • Affine ring-geometry
  • Central translation structure
  • Domains with a right GCD
  • Integral
  • Translation plane

ASJC Scopus subject areas

  • Mathematics(all)


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