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Mat. Sb. (N.S.), 1970, Volume 81(123), Number 1, Pages 132–144 (Mi msb3365)  

This article is cited in 16 scientific papers (total in 16 papers)

On a conjecture of Samuel

V. I. Danilov


Abstract: We construct examples disproving Samuel's conjecture stating that the ring $A[[T]]$ is factorial for a complete factorial local ring $A$. We also prove a theorem asserting (under some restrictions) that the ring $A[[T]]$ is factorial for a “'geometrically” factorial ring $A$.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1970, 10:1, 127–137

Bibliographic databases:

UDC: 513.015.7
MSC: 13F15, 13D03, 13H05, 51A10, 20J06
Received: 09.05.1969

Citation: V. I. Danilov, “On a conjecture of Samuel”, Mat. Sb. (N.S.), 81(123):1 (1970), 132–144; Math. USSR-Sb., 10:1 (1970), 127–137

Citation in format AMSBIB
\Bibitem{Dan70}
\by V.~I.~Danilov
\paper On~a~conjecture of Samuel
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 81(123)
\issue 1
\pages 132--144
\mathnet{http://mi.mathnet.ru/msb3365}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=252374}
\zmath{https://zbmath.org/?q=an:0197.03302|0215.07901}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 10
\issue 1
\pages 127--137
\crossref{https://doi.org/10.1070/SM1970v010n01ABEH001590}


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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. V. I. Danilov, “Rings with a discrete group of divisor classes”, Math. USSR-Sb., 12:3 (1970), 368–386  mathnet  crossref  mathscinet  zmath
    2. V. I. Danilov, “On rings with a discrete divisor class group”, Math. USSR-Sb., 17:2 (1972), 228–236  mathnet  crossref  mathscinet  zmath
    3. Hartshorne Robin, Ogus Arthur, “On the Factoriality of Local Rings of Small Embedding Codimension”, Communications in Algebra, 1:5 (1974), 415  crossref
    4. Hartmut Göhner, “Semifactoriality and Muhly's condition (N) in two dimensional local rings”, Journal of Algebra, 34:3 (1975), 403  crossref
    5. Robert Treger, “Reflexive modules”, Journal of Algebra, 54:2 (1978), 444  crossref
    6. Winfried Bruns, E. Graham Evans, Phillip A. Griffith, “Syzygies, ideals of height two, and vector bundles”, Journal of Algebra, 67:1 (1980), 143  crossref
    7. Ronald J. DiPerna, “Measure-valued solutions to conservation laws”, Arch Rational Mech Anal, 88:3 (1985), 223  crossref  mathscinet  zmath
    8. Lieven Le Bruyn, Alain Verschoren, “Maximal orders having a discrete normalizing class group”, Journal of Algebra, 100:2 (1986), 430  crossref
    9. Gui -Qiang Chen, “The method of quasidecoupling for discontinuous solutions to conservation laws”, Arch Rational Mech Anal, 121:2 (1992), 131  crossref  mathscinet  zmath
    10. E. Weinan, “Homogenization of linear and nonlinear transport equations”, Comm Pure Appl Math, 45:3 (1992), 301  crossref  mathscinet  zmath
    11. Alain Forestier, Philippe Floch, “Multivalued solutions to some non-linear and non-strictly hyperbolic systems”, Japan J Indust Appl Math, 9:1 (1992), 1  crossref
    12. Jinghua Wang, Gerald Warnecke, “On Entropy Consistency of Large Time Step Schemes II. Approximate Riemann Solvers”, SIAM J Numer Anal, 30:5 (1993), 1252  crossref  mathscinet  zmath  isi
    13. Claudia Miller, “Recovering divisor classes via their (T)-adic filtrations”, Journal of Pure and Applied Algebra, 127:3 (1998), 257  crossref
    14. Sandra Spiroff, “The limiting behavior on the restriction of divisor classes to hypersurfaces”, Journal of Pure and Applied Algebra, 186:1 (2004), 77  crossref
    15. Phillip Griffith, Sandra Spiroff, “Restriction of divisor classes to hypersurfaces in characteristic p”, Journal of Algebra, 275:2 (2004), 801  crossref
    16. Phillip Griffith, “Approximate liftings in local algebra and a theorem of Grothendieck”, Journal of Pure and Applied Algebra, 196:2-3 (2005), 185  crossref
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