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Algebra Logika, 2016, Volume 55, Number 2, Pages 219–256 (Mi al738)  

This article is cited in 5 scientific papers (total in 5 papers)

Equational conditions in universal algebraic geometry

P. Modabberi, M. Shahryari

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

Abstract: Different types of compactness in the Zariski topology are explored: for instance, being equational Noetherian, being equational Artinian, $q_\omega$- and $u_\omega$-compactness. Moreover, general results on the Zariski topology over algebras and groups are proved.

Keywords: algebraic structures, equations, algebraic sets, radical ideal, coordinate algebra, Zariski topology, equationally Noetherian algebras, $q_\omega$-compactness, $u_\omega$-compactness, metacompact algebras, metacompact spaces, equationally Artinian algebras, prevarieties, varieties, free algebras, equational domains, Hilbert's basis theorem.

DOI: https://doi.org/10.17377/alglog.2016.55.204

Full text: PDF file (273 kB)
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English version:
Algebra and Logic, 2016, 55:2, 146–172

Bibliographic databases:

UDC: 512.54.0+512.57
Received: 31.01.2014
Revised: 03.10.2015

Citation: P. Modabberi, M. Shahryari, “Equational conditions in universal algebraic geometry”, Algebra Logika, 55:2 (2016), 219–256; Algebra and Logic, 55:2 (2016), 146–172

Citation in format AMSBIB
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\by P.~Modabberi, M.~Shahryari
\paper Equational conditions in universal algebraic geometry
\jour Algebra Logika
\yr 2016
\vol 55
\issue 2
\pages 219--256
\mathnet{http://mi.mathnet.ru/al738}
\crossref{https://doi.org/10.17377/alglog.2016.55.204}
\transl
\jour Algebra and Logic
\yr 2016
\vol 55
\issue 2
\pages 146--172
\crossref{https://doi.org/10.1007/s10469-016-9384-7}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84982141363}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. Modabberi, M. Shahryari, “On the equational Artinian algebras”, Sib. elektron. matem. izv., 13 (2016), 875–881  mathnet  crossref
    2. Mohammad Shahryari, “Algebraic sets with fully characteristic radicals”, Zhurn. SFU. Ser. Matem. i fiz., 10:3 (2017), 293–297  mathnet  crossref
    3. M. Shahryari, A. Shevlyakov, “Direct products, varieties, and compactness conditions”, Groups Complex. Cryptol., 9:2 (2017), 159–166  crossref  mathscinet  zmath  isi  scopus
    4. Mahdiyeh Nouri, “Algebraic geometry over Heyting algebras”, Zhurn. SFU. Ser. Matem. i fiz., 13:4 (2020), 414–421  mathnet  crossref
    5. Mohammad Shahryari, Javad Tayyebi, “On the equationally Artinian groups”, Zhurn. SFU. Ser. Matem. i fiz., 13:5 (2020), 583–595  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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