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Mat. Sb. (N.S.), 1976, Volume 101(143), Number 3(11), Pages 334–348 (Mi msb2903)  

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

Ideals in commutative rings

Yu. A. Drozd


Abstract: This paper deals with one-dimensional (commutative) rings without nilpotent elements such that every ideal is generated by three elements. It is shown that in such rings the square of every ideal is invertible, i.e. divides its multiplier ring. In addition, every ideal is distinguished, in the sense that on localization at any maximal ideal it becomes either principal or dual to a principal ideal. Conversely, if a one-dimensional ring without nilpotent elements satisfies either of these conditions, and if all its residue class fields are $2$-perfect and contain at least three elements, then every ideal can be generated by three elements.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 30:3, 297–310

Bibliographic databases:

UDC: 519.48
MSC: Primary 13A15; Secondary 14A05, 14H20
Received: 18.11.1974

Citation: Yu. A. Drozd, “Ideals in commutative rings”, Mat. Sb. (N.S.), 101(143):3(11) (1976), 334–348; Math. USSR-Sb., 30:3 (1976), 297–310

Citation in format AMSBIB
\Bibitem{Dro76}
\by Yu.~A.~Drozd
\paper Ideals in commutative rings
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 101(143)
\issue 3(11)
\pages 334--348
\mathnet{http://mi.mathnet.ru/msb2903}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=427300}
\zmath{https://zbmath.org/?q=an:0339.13015}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 30
\issue 3
\pages 297--310
\crossref{https://doi.org/10.1070/SM1976v030n03ABEH002275}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976FN58700002}


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  • http://mi.mathnet.ru/eng/msb/v143/i3/p334

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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. Drozd Yu.A., Skuratovskii R.V., “Cubic Rings and their Ideals”, Ukr. Math. J., 62:4 (2010), 530–536  crossref  mathscinet  zmath  isi
    2. Yuriy A. Drozd, Ruslan V. Skuratovskii, “One branch curve singularities with at most 2-parameter families of ideals”, Algebra Discrete Math., 13:2 (2012), 209–219  mathnet  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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