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Sibirsk. Mat. Zh., 2017, Volume 58, Number 5, Pages 1035–1050 (Mi smj2917)  

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

Universal geometrical equivalence of the algebraic structures of common signature

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

a 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.

Funding Agency Grant Number
Russian Science Foundation 17-11-01117
The authors were supported by the Russian Science Foundation (Grant 17-11-01117).


DOI: https://doi.org/10.17377/smzh.2017.58.507

Full text: PDF file (360 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 510.67+512.71
MSC: 35R30
Received: 09.06.2017

Citation: E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Universal geometrical equivalence of the algebraic structures of common signature”, Sibirsk. Mat. Zh., 58:5 (2017), 1035–1050; Siberian Math. J., 58:5 (2017), 801–812

Citation in format AMSBIB
\Bibitem{DanMyaRem17}
\by E.~Yu.~Daniyarova, A.~G.~Myasnikov, V.~N.~Remeslennikov
\paper Universal geometrical equivalence of the algebraic structures of common signature
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 5
\pages 1035--1050
\mathnet{http://mi.mathnet.ru/smj2917}
\crossref{https://doi.org/10.17377/smzh.2017.58.507}
\elib{http://elibrary.ru/item.asp?id=29947470}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 5
\pages 801--812
\crossref{https://doi.org/10.1134/S003744661705007X}
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\elib{http://elibrary.ru/item.asp?id=31068917}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85032018682}


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    Citing articles on Google Scholar: Russian citations, English citations
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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
  • Сибирский математический журнал Siberian Mathematical Journal
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