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Algebra Logika, 2017, Volume 56, Number 4, Pages 421–442 (Mi al806)  

This article is cited in 2 scientific papers (total in 2 papers)

Algebraic geometry over algebraic structures. VI. Geometric equivalence

E. Yu. Daniyarovaa, A. G. Myasnikovb, V. N. Remeslennikova

a 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00068-а
Supported by RFBR, project No. 14-01-00068-a.


DOI: https://doi.org/10.17377/alglog.2017.56.403

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

Bibliographic databases:

UDC: 510.67+512.71
Received: 21.08.2015
Revised: 14.05.2016

Citation: E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VI. Geometric equivalence”, Algebra Logika, 56:4 (2017), 421–442; Algebra and Logic, 56:4 (2017), 281–294

Citation in format AMSBIB
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\by E.~Yu.~Daniyarova, A.~G.~Myasnikov, V.~N.~Remeslennikov
\paper Algebraic geometry over algebraic structures.~VI. Geometric equivalence
\jour Algebra Logika
\yr 2017
\vol 56
\issue 4
\pages 421--442
\mathnet{http://mi.mathnet.ru/al806}
\crossref{https://doi.org/10.17377/alglog.2017.56.403}
\transl
\jour Algebra and Logic
\yr 2017
\vol 56
\issue 4
\pages 281--294
\crossref{https://doi.org/10.1007/s10469-017-9449-2}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85033406089}


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    This publication is cited in the following articles:
    1. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits”, Algebra and Logic, 57:6 (2019), 414–428  mathnet  crossref  crossref  isi
    2. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures X: ordinal dimension”, Int. J. Algebr. Comput., 28:8, SI (2018), 1425–1448  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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