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, 2018, Volume 57, Number 6, Pages 639–661
DOI: https://doi.org/10.33048/alglog.2018.57.602
(Mi al872)
 

This article is cited in 4 scientific papers (total in 4 papers)

Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits

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
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 (284 kB) Citations (4)
References:
Abstract: This paper enters into a series of works on universal algebraic geometry — a branch of mathematics that is presently flourishing and is still undergoing active development. The theme and subject area of universal algebraic geometry have their origins in classical algebraic geometry over a field, while the language and almost the entire methodological apparatus belong to model theory and universal algebra. The focus of the paper is the problem of finding Dis-limits for a given algebraic structure $\mathcal{A}$, i.e., algebraic structures in which all irreducible coordinate algebras over $\mathcal{A}$ are embedded and in which there are no other finitely generated substructures. Finding a solution to this problem necessitated a good description of principal universal classes and quasivarieties. The paper is divided into two parts. In the first part, we give criteria for a given universal class (or quasivariety) to be principal. In the second part, we formulate explicitly the problem of finding Dis-limits for algebraic structures and show how the results of the first part make it possible to solve this problem in many cases.
Keywords: universal algebraic geometry, algebraic structure, universal class, quasivariety, joint embedding property, irreducible coordinate algebra, discriminability, Dis-limit, equational Noetherian property, equational codomain, universal geometric equivalence.
Funding agency Grant number
Russian Science Foundation 17-11-01117
Received: 06.02.2017
Revised: 10.10.2017
English version:
Algebra and Logic, 2019, Volume 57, Issue 6, Pages 414–428
DOI: https://doi.org/10.1007/s10469-019-09514-6
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. IX. Principal Universal Classes and Dis-Limits”, Algebra Logika, 57:6 (2018), 639–661; Algebra and Logic, 57:6 (2019), 414–428
Citation in format AMSBIB
\Bibitem{DanMyaRem18}
\by E.~Yu.~Daniyarova, A.~G.~Myasnikov, V.~N.~Remeslennikov
\paper Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits
\jour Algebra Logika
\yr 2018
\vol 57
\issue 6
\pages 639--661
\mathnet{http://mi.mathnet.ru/al872}
\crossref{https://doi.org/10.33048/alglog.2018.57.602}
\transl
\jour Algebra and Logic
\yr 2019
\vol 57
\issue 6
\pages 414--428
\crossref{https://doi.org/10.1007/s10469-019-09514-6}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000463584500002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85063965160}
Linking options:
  • https://www.mathnet.ru/eng/al872
  • https://www.mathnet.ru/eng/al/v57/i6/p639
    Cycle of papers
    This publication is cited in the following 4 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:358
    Full-text PDF :28
    References:50
    First page:14
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024