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Mathematics of the USSR-Izvestiya, 1980, Volume 14, Issue 1, Pages 41–60
DOI: https://doi.org/10.1070/IM1980v014n01ABEH001070
(Mi im1578)
 

This article is cited in 27 scientific papers (total in 28 papers)

Local description of closed ideals and submodules of analytic functions of one variable. I

I. F. Krasichkov-Ternovskii
References:
Abstract: Let $P$ be a topological module (over the ring of polynomials) of vector-valued functions $f\colon G\to\mathbf C^q$, holomorphic in a domain $G\subset\mathbf C$.
A closed submodule $I\subset P$ is local (that is, uniquely determined by the collection $I_\lambda$, $\lambda\in G$, of its localized submodules) if and only if $I$ is stable and saturated. A submodule is said to be stable if it admits division by binomials: $f\in I$, $\frac f{z-\lambda}\in I_\lambda\Rightarrow\frac f{z-\lambda}\in I$.
Being saturated amounts to possessing sufficiently many elements.
Bibliography: 26 titles.
Received: 20.12.1976
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1979, Volume 43, Issue 1, Pages 44–66
Bibliographic databases:
UDC: 517.5
MSC: 46J15, 46J20
Language: English
Original paper language: Russian
Citation: I. F. Krasichkov-Ternovskii, “Local description of closed ideals and submodules of analytic functions of one variable. I”, Izv. Akad. Nauk SSSR Ser. Mat., 43:1 (1979), 44–66; Math. USSR-Izv., 14:1 (1980), 41–60
Citation in format AMSBIB
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\by I.~F.~Krasichkov-Ternovskii
\paper Local description of closed ideals and submodules of analytic functions of one variable.~I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 1
\pages 44--66
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=525941}
\zmath{https://zbmath.org/?q=an:0433.46048|0404.46037}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 1
\pages 41--60
\crossref{https://doi.org/10.1070/IM1980v014n01ABEH001070}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980KM22000003}
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  • https://doi.org/10.1070/IM1980v014n01ABEH001070
  • https://www.mathnet.ru/eng/im/v43/i1/p44
    Cycle of papers
    This publication is cited in the following 28 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
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    Abstract page:370
    Russian version PDF:116
    English version PDF:10
    References:55
    First page:2
     
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