This article is cited in 9 papers

Algebraic geometry over algebraic structures. VI. Geometric equivalence

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

a</sup> Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099 Russia
^b Schaefer School of Engineering and Science, Dep. of Math. Sci., Stevens Institute of Technology, Castle Point on Hudson, Hoboken NJ 07030-5991, USA

Abstract: The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures $\mathcal A$ and $\mathcal B$ of a language $\mathrm L$, the classification problems for algebraic sets over $\mathcal A$ and $\mathcal B$ are equivalent. We establish a connection between geometrical equivalence and quasi-equational equivalence.

Keywords: universal algebraic geometry, algebraic structure, geometrical equivalence, prevariety, quasivariety.

UDC: 510.67+512.71

Received: 21.08.2015
Revised: 14.05.2016

DOI: 10.17377/alglog.2017.56.403

 English version: Algebra and Logic, 2017, 56:4, 281–294

Bibliographic databases:

• 
•