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Algebra i logika, 2017, Volume 56, Number 4, Pages 421–442
DOI: https://doi.org/10.17377/alglog.2017.56.403 (Mi al806) 		 
This article is cited in 9 scientific papers (total in 9 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
Full-text PDF (228 kB) Citations (9)
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DOI: https://doi.org/10.17377/alglog.2017.56.403
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.
Received: 21.08.2015
Revised: 14.05.2016
English version:
Algebra and Logic, 2017, Volume 56, Issue 4, Pages 281–294
DOI: https://doi.org/10.1007/s10469-017-9449-2
Bibliographic databases:
Document Type: Article
UDC: 510.67+512.71
Language: Russian
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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85033406089}
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    Cycle of papers
    This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и логика Algebra and Logic
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    Full-text PDF :108
    References:53
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