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Mat. Zametki, 1976, Volume 19, Issue 6, Pages 843–851 (Mi mz7805)  

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

Regular completion of modules

V. K. Zakharov

Leningrad Institute for Textile and Light Industry

Abstract: In this paper we introduce the concept of a module regular in the sense of von Neumann. We construct a regular completion of a module $X$ torsion-free relative to a filter $\mathfrak F_R$of dense modules over a commutative semiprimary ring $R$. The paper's main result is a theorem that module $X$ is divisible (is injective relative to filter $\mathfrak F_R$) if and only if it is von Neumann-regular and orthocomplete. We prove that a divisible hull of module $X$ relative to $\mathfrak F_R$ is a composition of two simpler completions: a regular one and an orthocompletion.

Full text: PDF file (786 kB)

English version:
Mathematical Notes, 1976, 19:6, 496–500

Bibliographic databases:

UDC: 519.4
Received: 19.05.1975

Citation: V. K. Zakharov, “Regular completion of modules”, Mat. Zametki, 19:6 (1976), 843–851; Math. Notes, 19:6 (1976), 496–500

Citation in format AMSBIB
\Bibitem{Zak76}
\by V.~K.~Zakharov
\paper Regular completion of modules
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 6
\pages 843--851
\mathnet{http://mi.mathnet.ru/mz7805}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=422332}
\zmath{https://zbmath.org/?q=an:0338.13011|0336.13006}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 6
\pages 496--500
\crossref{https://doi.org/10.1007/BF01149925}


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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. V. K. Zakharov, “The divisible hull and orthocompletion of lattice ordered modules”, Math. USSR-Sb., 32:3 (1977), 293–303  mathnet  crossref  mathscinet  zmath  isi
    2. K. I. Beidar, A. V. Mikhalev, “Orthogonal completeness and algebraic systems”, Russian Math. Surveys, 40:6 (1985), 51–95  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математические заметки Mathematical Notes
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