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Diskretnaya Matematika, 2017, Volume 29, Issue 3, Pages 126–132
DOI: https://doi.org/10.4213/dm1421 (Mi dm1421) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Arithmetical rings and Krull dimension

A. A. Tuganbaev

National Research University "Moscow Power Engineering Institute"
Full-text PDF (387 kB) Citations (2)
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DOI: https://doi.org/10.4213/dm1421
Abstract: Let $A$ be a commutative arithmetical ring. It is proved that the ring $A$ has Krull dimension if and only if every factor ring of $A$ is finite-dimensional and does not have idempotent proper essential ideals.
Keywords: arithmetical ring, Krull dimension, idempotent ideal.
Funding agency Grant number
Russian Science Foundation 16-11-10013
Исследование выполнено за счет Российского научного фонда (проект 16-11-10013).
Received: 29.11.2016
English version:
Discrete Mathematics and Applications, 2018, Volume 28, Issue 2, Pages 113–117
DOI: https://doi.org/10.1515/dma-2018-0011
Bibliographic databases:
Document Type: Article
UDC: 512.55
Language: Russian
Citation: A. A. Tuganbaev, “Arithmetical rings and Krull dimension”, Diskr. Mat., 29:3 (2017), 126–132; Discrete Math. Appl., 28:2 (2018), 113–117
Citation in format AMSBIB
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\paper Arithmetical rings and Krull dimension
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\yr 2017
\vol 29
\issue 3
\pages 126--132
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\transl
\jour Discrete Math. Appl.
\yr 2018
\vol 28
\issue 2
\pages 113--117
\crossref{https://doi.org/10.1515/dma-2018-0011}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045686997}
Linking options:
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  • https://doi.org/10.4213/dm1421
  • https://www.mathnet.ru/eng/dm/v29/i3/p126
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретная математика
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    Full-text PDF :54
    References:31
    First page:19
     
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