Two notes on the axiomatics of structures with parallelism

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)93-104
Number of pages12
JournalNote di Matematica
Volume20
Issue number2
StatePublished - 2001

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Axiomatization
Parallelism
Affine geometry
Highest common factor
Zero-divisor
Translation Planes
Quantifiers
First-order
Ring

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Two notes on the axiomatics of structures with parallelism. / Pambuccian, Victor.

In: Note di Matematica, Vol. 20, No. 2, 2001, p. 93-104.

Research output: Contribution to journalArticle

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