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Fundam. Prikl. Mat., 2014, Volume 19, Issue 2, Pages 21–23 (Mi fpm1575)  

This article is cited in 3 scientific papers (total in 4 papers)

A remark on commutative arithmetic rings

E. S. Golod

Lomonosov Moscow State University, Moscow, Russia

Abstract: It is proved that a commutative ring with identity $R$ is arithmetic (i.e., the ideal lattice of $R$ is distributive) if and only if for any finitely generated (or any finitely presented) $R$-module $M$ and any ideal $I$ of $R$ the equality $I+\operatorname{Ann}M=\operatorname{Ann}(M/IM)$ holds.

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English version:
Journal of Mathematical Sciences (New York), 2016, 213:2, 143–144

Bibliographic databases:

UDC: 512.55

Citation: E. S. Golod, “A remark on commutative arithmetic rings”, Fundam. Prikl. Mat., 19:2 (2014), 21–23; J. Math. Sci., 213:2 (2016), 143–144

Citation in format AMSBIB
\Bibitem{Gol14}
\by E.~S.~Golod
\paper A~remark on commutative arithmetic rings
\jour Fundam. Prikl. Mat.
\yr 2014
\vol 19
\issue 2
\pages 21--23
\mathnet{http://mi.mathnet.ru/fpm1575}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431913}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 213
\issue 2
\pages 143--144
\crossref{https://doi.org/10.1007/s10958-016-2706-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84954482372}


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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. E. S. Golod, A. A. Tuganbaev, “Annihilators and finitely generated modules”, J. Math. Sci., 233:5 (2018), 656–658  mathnet  crossref
    2. A. A. Tuganbaev, “Bezout rings, annihilators, and diagonalizability”, J. Math. Sci., 237:2 (2019), 329–331  mathnet  crossref
    3. A. A. Tuganbaev, “Arifmeticheskie koltsa”, Algebra, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 164, VINITI RAN, M., 2019, 3–73  mathnet  mathscinet
    4. V. A. Artamonov, V. M. Buchstaber, È. B. Vinberg, L. V. Kuz'min, V. S. Kulikov, V. N. Latyshev, A. V. Mikhalev, A. Yu. Ol'shanskii, D. O. Orlov, A. N. Parshin, D. I. Piontkovskii, “Evgenii Solomonovich Golod (obituary)”, Russian Math. Surveys, 74:5 (2019), 927–933  mathnet  crossref  crossref  adsnasa  isi
  • Фундаментальная и прикладная математика
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