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Mat. Zametki, 2015, Volume 97, Issue 6, Pages 925–929 (Mi mz10222)  

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

Characterization of Locally Noetherian Varieties in Terms of Idempotents

O. B. Finogenova

Ural State University, Ekaterinburg

Abstract: It is proved that a variety of associative rings is left and right locally Noetherian if and only if every finitely generated ring in the variety contains only finitely many idempotents.

Keywords: variety of associative rings, left (right) locally Noetherian ring, idempotent.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00524
Ministry of Education and Science of the Russian Federation 2248
НШ-5161.2014.1
This work was completed in the framework of the implementation of the basic part of the State Assignment concerning the completion of Scientific Research Developments (grant no. 2248 of the Ministry of Education and Science of the Russian Federation) and was supported by the Russian Foundation for Basic Research (grant no. 14-01-00524) and by the program “Leading Scientific Schools” (grant no. NSh-5161.2014.1).


DOI: https://doi.org/10.4213/mzm10222

Full text: PDF file (409 kB)
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English version:
Mathematical Notes, 2015, 97:6, 937–940

Bibliographic databases:

Document Type: Article
UDC: 512.552.4
Received: 08.11.2012

Citation: O. B. Finogenova, “Characterization of Locally Noetherian Varieties in Terms of Idempotents”, Mat. Zametki, 97:6 (2015), 925–929; Math. Notes, 97:6 (2015), 937–940

Citation in format AMSBIB
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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. Finogenova O.B., “Varieties satisfying semigroup identities: Algebras over a finite field and rings”, Int. J. Algebr. Comput., 26:5 (2016), 985–1017  crossref  mathscinet  zmath  isi  elib  scopus
    2. Volkov M.V., Silva P.V., Soares F., “Local Finiteness For Green'S Relations in Semigroup Varieties”, Commun. Algebr., 46:11 (2018), 4625–4653  crossref  mathscinet  zmath  isi  scopus
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