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Mathematics of the USSR-Izvestiya, 1980, Volume 15, Issue 3, Pages 589–623
DOI: https://doi.org/10.1070/IM1980v015n03ABEH001270 (Mi im1759) 		 
This article is cited in 22 scientific papers (total in 22 papers)

Reciprocity laws and the stable rank of polynomial rings

A. A. Suslin
English version PDF (1734 kB) Citations (22)
References:
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DOI: https://doi.org/10.1070/IM1980v015n03ABEH001270
Abstract: Reciprocity laws and Mennicke symbols for regular rings of arbitrary dimension are introduced and studied. The universal Mennicke symbol for the polynomial ring $k[X_1,\dots,X_n]$ relative to the principal ideal $(X_1^2-X_1)\cdots(X_n^2-X_n)$ is computed. The results obtained in this paper are applied to the problem of determining the precise value of the stable rank of polynomial rings and affine algebras over fields.
Bibliography: 19 titles.
Received: 19.10.1978
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1979, Volume 43, Issue 6, Pages 1394–1429
Bibliographic databases:
UDC: 519.4
MSC: Primary 13D15; Secondary 13F20
Language: English
Original paper language: Russian
Citation: A. A. Suslin, “Reciprocity laws and the stable rank of polynomial rings”, Izv. Akad. Nauk SSSR Ser. Mat., 43:6 (1979), 1394–1429; Math. USSR-Izv., 15:3 (1980), 589–623
Citation in format AMSBIB
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\by A.~A.~Suslin
\paper Reciprocity laws and the stable rank of polynomial rings
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 6
\pages 1394--1429
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\zmath{https://zbmath.org/?q=an:0452.13007|0428.13007}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 3
\pages 589--623
\crossref{https://doi.org/10.1070/IM1980v015n03ABEH001270}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980LF66600007}
Linking options:
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  • https://doi.org/10.1070/IM1980v015n03ABEH001270
  • https://www.mathnet.ru/eng/im/v43/i6/p1394
    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:649
    Russian version PDF:303
    English version PDF:33
    References:58
    First page:3
     
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