This article is cited in 3 papers

Universal geometrical equivalence of the algebraic structures of common signature

E. Yu. Daniyarova^a, A. G. Myasnikov^b, V. N. Remeslennikov<sup>a

a</sup> Sobolev Institute of Mathematics, Omsk Branch, Omsk, Russia
^b School of Engineering & Science, Stevens Institute of Technology, Hoboken NJ, USA

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 $\mathscr A$ and $\mathscr B$ of a common language {\tt L} which strengthens the available concept of geometrical equivalence and expresses the maximal affinity between $\mathscr A$ and $\mathscr B$ 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.

Keywords: universal algebraic geometry, algebraic structure, universal geometrical equivalence, universal equivalence, universal class.

UDC: 510.67+512.71

MSC: 35R30

Received: 09.06.2017

DOI: 10.17377/smzh.2017.58.507

 English version: Siberian Mathematical Journal, 2017, 58:5, 801–812

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