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Mat. Sb., 1991, Volume 182, Number 9, Pages 1251–1260 (Mi msb1352)  

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

Noncommutative Prüfer rings

N. I. Dubrovin


Abstract: The concept of a Prüfer ring is generalized to orders in simple Artinian rings so that the new concept gives a minimal class of rings closed under Morita equivalence, but in the commutative case does not extend the class of Prüfer domains.
In § 1 this problem is solved and some elementary properties of noncommutative Prüfer rings are given. In § 2 theorems on the localization of a noncommutative Prüfer ring with respect to a prime ideal are proved, these being the basis of the theory. In § 3 noncommutative Prüfer rings in a simple finite-dimensional algebra over a field are considered. The main problem, which is posed and partially solved here, involves the connection between a noncommutative Prüfer ring and its center.

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English version:
Mathematics of the USSR-Sbornik, 1993, 74:1, 1–8

Bibliographic databases:

UDC: 519.48
MSC: Primary 16P20, 16H05; Secondary 16P50, 16K20
Received: 10.05.1990

Citation: N. I. Dubrovin, “Noncommutative Prüfer rings”, Mat. Sb., 182:9 (1991), 1251–1260; Math. USSR-Sb., 74:1 (1993), 1–8

Citation in format AMSBIB
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\by N.~I.~Dubrovin
\paper Noncommutative Pr\"ufer rings
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 9
\pages 1251--1260
\mathnet{http://mi.mathnet.ru/msb1352}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1133567}
\zmath{https://zbmath.org/?q=an:0793.16021}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993SbMat..74....1D}
\transl
\jour Math. USSR-Sb.
\yr 1993
\vol 74
\issue 1
\pages 1--8
\crossref{https://doi.org/10.1070/SM1993v074n01ABEH003330}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993KQ22500001}


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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. H. H. Brungs, J. Gräter, “Orders of Higher Rank in Semisimple Artinian Rings”, Math Nachr, 182:1 (1996), 73  crossref  mathscinet  zmath  isi
    2. Hidetoshi Marybayashi, Zhong Yi, “Dubrovin valuation properties of skew group rings and crossed products”, Communications in Algebra, 26:1 (1998), 293  crossref
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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