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Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 875–881 (Mi semr719)  

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

Mathematical logic, algebra and number theory

On the equational Artinian algebras

P. Modabberi, M. Shahryari

Department of Pure Mathematics, University of Tabriz, Tabriz, Iran

Abstract: Equational Artinian algebras were introduced in our previous work: Compactness conditions in universal algebraic geometry, Algebra and Logic, 2016, 55 (2). In this note, we define the notion of radical topology with respect to an algebra $A$ and using the well-known König lemma in graph theory, we show that the algebra $A$ is equational Artinian iff this topology is Noetherian. This completes the analogy between equational Noetherian and equational Artinian algebras.

Keywords: algebraic structures, equations, algebraic sets, radical ideals, coordinate algebras, Zariski topology, equationally Noetherian algebras, equational Artinian algebras; radical topology.

DOI: https://doi.org/10.17377/semi.2016.13.069

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Bibliographic databases:

UDC: 512.71+512.55
MSC: 03C99,08A99,14A99
Received February 29, 2016, published October 14, 2016
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Citation: P. Modabberi, M. Shahryari, “On the equational Artinian algebras”, Sib. Èlektron. Mat. Izv., 13 (2016), 875–881

Citation in format AMSBIB
\Bibitem{ModSha16}
\by P.~Modabberi, M.~Shahryari
\paper On the equational Artinian algebras
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 875--881
\mathnet{http://mi.mathnet.ru/semr719}
\crossref{https://doi.org/10.17377/semi.2016.13.069}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000407781100069}


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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. Mahdiyeh Nouri, “Algebraic geometry over Heyting algebras”, Zhurn. SFU. Ser. Matem. i fiz., 13:4 (2020), 414–421  mathnet  crossref
    2. Mohammad Shahryari, Javad Tayyebi, “On the equationally Artinian groups”, Zhurn. SFU. Ser. Matem. i fiz., 13:5 (2020), 583–595  mathnet  crossref
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