Algebra i logika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra i logika, 2012, Volume 51, Number 1, Pages 41–60 (Mi al521)  

This article is cited in 24 scientific papers (total in 24 papers)

Algebraic geometry over algebraic structures. V. The case of arbitrary signature

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

a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Omsk, Russia
b Schaefer School of Engineering and Science, Dep. of Math. Sci., Stevens Institute of Technology, Hoboken, NJ, USA
References:
Abstract: A general theory of algebraic geometry over an arbitrary algebraic structure $\mathcal A$ in a language $\mathrm L$ with no predicates is consistently presented in a series of papers on universal algebraic geometry [B. Fine (ed.) et al., Aspects of infinite groups. A Festschrift in honor of A. Gaglione (Papers of the conf., Fairfield, USA, March 2007 in honour of A. Gaglione's 60th birthday), (Algebra Discr. Math. (Hackensack), 1), Hackensack, NJ, World Sci., 2008, 80–111; submitted to Fund. Appl. Math.; Southeast Asian Bull. Math., accepted for publ.; Algebra i Logika, 49, No. 6 (2010), 715–756]. The restriction that we impose on the language is not crucial. This is done for the sake of readers who only get acquainted with universal algebraic geometry. Here we show how the entire material accumulated in works on universal geometry can be carried over without essential changes to the case of an arbitrary signature $\mathrm L$.
Keywords: universal algebraic geometry, algebraic structure, algebraic set, coordinate algebra.
Received: 23.05.2011
English version:
Algebra and Logic, 2012, Volume 51, Issue 1, Pages 28–40
DOI: https://doi.org/10.1007/s10469-012-9168-7
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. V. The case of arbitrary signature”, Algebra Logika, 51:1 (2012), 41–60; Algebra and Logic, 51:1 (2012), 28–40
Citation in format AMSBIB
\Bibitem{DanMyaRem12}
\by E.~Yu.~Daniyarova, A.~G.~Myasnikov, V.~N.~Remeslennikov
\paper Algebraic geometry over algebraic structures.~V. The case of arbitrary signature
\jour Algebra Logika
\yr 2012
\vol 51
\issue 1
\pages 41--60
\mathnet{http://mi.mathnet.ru/al521}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2986463}
\zmath{https://zbmath.org/?q=an:1255.08001}
\transl
\jour Algebra and Logic
\yr 2012
\vol 51
\issue 1
\pages 28--40
\crossref{https://doi.org/10.1007/s10469-012-9168-7}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000304163300002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84861839130}
Linking options:
  • https://www.mathnet.ru/eng/al521
  • https://www.mathnet.ru/eng/al/v51/i1/p41
    Cycle of papers
    This publication is cited in the following 24 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
    Statistics & downloads:
    Abstract page:639
    Full-text PDF :166
    References:64
    First page:14
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024