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Universal geometrical equivalence of the algebraic structures of common signature

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Omsk Branch, Omsk, Russia

    E. Yu. Daniyarova & V. N. Remeslennikov

  2. Stevens Institute of Technology, Hoboken, USA

    A. G. Myasnikov

Authors
  1. E. Yu. Daniyarova
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  2. A. G. Myasnikov
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  3. V. N. Remeslennikov
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Correspondence to E. Yu. Daniyarova.

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Original Russian Text Copyright © 2017 Daniyarova E.Yu., Myasnikov A.G., and Remeslennikov V.N.

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 5, pp. 1035–1050, September–October, 2017; DOI: 10.17377/smzh.2017.58.507.

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Daniyarova, E.Y., Myasnikov, A.G. & Remeslennikov, V.N. Universal geometrical equivalence of the algebraic structures of common signature. Sib Math J 58, 801–812 (2017). https://doi.org/10.1134/S003744661705007X

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  • DOI: https://doi.org/10.1134/S003744661705007X

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