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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 5, Pages 1035–1050
DOI: https://doi.org/10.17377/smzh.2017.58.507
(Mi smj2917)
 

This article is cited in 3 scientific papers (total in 3 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
Full-text PDF (360 kB) Citations (3)
References:
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).
Received: 09.06.2017
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 5, Pages 801–812
DOI: https://doi.org/10.1134/S003744661705007X
Bibliographic databases:
Document Type: Article
UDC: 510.67+512.71
MSC: 35R30
Language: Russian
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
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\pages 1035--1050
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\transl
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  • https://www.mathnet.ru/eng/smj/v58/i5/p1035
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Full-text PDF :180
    References:44
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