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Mat. Sb. (N.S.), 1972, Volume 88(130), Number 2(6), Pages 229–237 (Mi msb3155)  

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

On rings with a discrete divisor class group

V. I. Danilov


Abstract: We consider the conjecture: $C(A)=C(A[[T]])$ for a local ring $A$ if and only if the divisor class group of the strict henselization $C(^\mathrm{sh}A)$ has a finite number of generators. This conjecture is proved in two cases: 1) $A$ has characteristic $0$, 2) $A$ is an equicharacteristic ring of an isolated singularity.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 17:2, 228–236

Bibliographic databases:

UDC: 513 015.7
MSC: Primary 13J15, 13F15; Secondary 14L15
Received: 07.04.1971

Citation: V. I. Danilov, “On rings with a discrete divisor class group”, Mat. Sb. (N.S.), 88(130):2(6) (1972), 229–237; Math. USSR-Sb., 17:2 (1972), 228–236

Citation in format AMSBIB
\Bibitem{Dan72}
\by V.~I.~Danilov
\paper On~rings with a~discrete divisor class group
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 88(130)
\issue 2(6)
\pages 229--237
\mathnet{http://mi.mathnet.ru/msb3155}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=306184}
\zmath{https://zbmath.org/?q=an:0251.13001}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 17
\issue 2
\pages 228--236
\crossref{https://doi.org/10.1070/SM1972v017n02ABEH001501}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Winfried Bruns, E. Graham Evans, Phillip A. Griffith, “Syzygies, ideals of height two, and vector bundles”, Journal of Algebra, 67:1 (1980), 143  crossref
    2. Frank R DeMeyer, Timothy J Ford, “On the Brauer group of surfaces”, Journal of Algebra, 86:1 (1984), 259  crossref
    3. Lieven Le Bruyn, Alain Verschoren, “Maximal orders having a discrete normalizing class group”, Journal of Algebra, 100:2 (1986), 430  crossref
    4. Claudia Miller, “Recovering divisor classes via their (T)-adic filtrations”, Journal of Pure and Applied Algebra, 127:3 (1998), 257  crossref
    5. Amiram Braun, Charudatta R. Hajarnavis, “Smooth polynomial identity algebras with almost factorial centers”, Journal of Algebra, 299:1 (2006), 124  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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