Universal geometrical equivalence of the algebraic structures of common signature

E. Yu Daniyarova, A. G. Myasnikov, V. N. Remeslennikov

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Abstract

This article is a part of our effort to explain the foundations of algebraic geometry over arbitrary algebraic structures [1–8]. We introduce the concept of universal geometrical equivalence of two algebraic structures A and B of a common language L which strengthens the available concept of geometrical equivalence and expresses the maximal affinity between A and B from the viewpoint of their algebraic geometries. We establish a connection between universal geometrical equivalence and universal equivalence in the sense of equality of universal theories.

Original languageEnglish
Pages (from-to)801-812
Number of pages12
JournalSiberian Mathematical Journal
Volume58
Issue number5
DOIs
StatePublished - 1 Sep 2017

Keywords

  • algebraic structure
  • universal algebraic geometry
  • universal class
  • universal equivalence
  • universal geometrical equivalence

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