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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 4(8), Pages 544–559 (Mi msb2415)  

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

Integrally closed rings

A. A. Tuganbaev


Abstract: This paper studies integrally closed rings. It is shown that a semiprime integrally closed Goldie ring is the direct product of a semisimple Artinian ring and a finite number of integrally closed invariant domains that are classically integrally closed in their (division) rings of fractions. It is shown also that an integrally closed ring has a classical ring of fractions and is classically integrally closed in it.
Next, integrally closed Noetherian rings are considered. It is shown that an integrally closed Noetherian ring all of whose nonzero prime ideals are maximal is either a quasi-Frobenius ring or a hereditary invariant domain.
Finally, those Noetherian rings all of whose factor rings are invariant are described, and the connection between integrally closed rings and distributive rings is examined.
Bibliography: 13 titles.

Full text: PDF file (1857 kB)
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English version:
Mathematics of the USSR-Sbornik, 1982, 43:4, 485–498

Bibliographic databases:

UDC: 512.552
MSC: Primary 16A08, 16A14, 16A30, 16A33, 16A34, 16A52; Secondary 13B20
Received: 28.04.1980

Citation: A. A. Tuganbaev, “Integrally closed rings”, Mat. Sb. (N.S.), 115(157):4(8) (1981), 544–559; Math. USSR-Sb., 43:4 (1982), 485–498

Citation in format AMSBIB
\Bibitem{Tug81}
\by A.~A.~Tuganbaev
\paper Integrally closed rings
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 4(8)
\pages 544--559
\mathnet{http://mi.mathnet.ru/msb2415}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=629626}
\zmath{https://zbmath.org/?q=an:0492.16007|0473.16002}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 4
\pages 485--498
\crossref{https://doi.org/10.1070/SM1982v043n04ABEH002576}


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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. Alajbegovic J., Dubrovin N., “Noncommutative Prufer-Rings”, J. Algebra, 135:1 (1990), 165–176  crossref  mathscinet  zmath  isi
    2. A. A. Tuganbaev, “Plane modules and distributivity”, Russian Math. Surveys, 50:6 (1995), 1314–1315  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. A. Tuganbaev, “Distributively decomposable rings”, Russian Math. Surveys, 51:3 (1996), 569–570  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. A. A. Tuganbaev, “Avtomorfizm-prodolzhaemye i endomorfizm-prodolzhaemye moduli”, Fundament. i prikl. matem., 21:4 (2016), 175–248  mathnet  mathscinet
    5. A. N. Abyzov, Ch. K. Kuin, A. A. Tuganbaev, “Moduli, invariantnye otnositelno avtomorfizmov i idempotentnykh endomorfizmov svoikh obolochek i nakrytii”, Algebra, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 159, VINITI RAN, M., 2019, 3–45  mathnet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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