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Vladikavkaz. Mat. Zh., 2014, Volume 16, Number 2, Pages 69–78 (Mi vmj506)  

This article is cited in 1 scientific paper (total in 1 paper)

Laterally complete $C_\infty(Q)$-modules

V. I. Chilina, J. A. Karimovb

a National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan
b National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan

Abstract: Let $X$ be a regular laterally complete $C_\infty(Q)$-module and $\mathscr B$ be a Boolean algebra whose Stone space is $Q$. We introduce the passport $\Gamma(X)$ for $X$ consisting of uniquely defined partition of unity in $\mathscr B$ and set of pairwise different cardinal numbers. It is proved that $C_\infty(Q)$-modules $X$ and $Y$ are isomorphic if and only if $\Gamma(X)=\Gamma(Y)$.

Key words: Hamel $C_\infty(Q)$-basis, homogeneous module, $\sigma$-finite dimensional module.

Full text: PDF file (251 kB)
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UDC: 512.55
Received: 27.11.2012

Citation: V. I. Chilin, J. A. Karimov, “Laterally complete $C_\infty(Q)$-modules”, Vladikavkaz. Mat. Zh., 16:2 (2014), 69–78

Citation in format AMSBIB
\Bibitem{ChiKar14}
\by V.~I.~Chilin, J.~A.~Karimov
\paper Laterally complete $C_\infty(Q)$-modules
\jour Vladikavkaz. Mat. Zh.
\yr 2014
\vol 16
\issue 2
\pages 69--78
\mathnet{http://mi.mathnet.ru/vmj506}


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    This publication is cited in the following articles:
    1. V. I. Chilin, J. A. Karimov, “Strictly homogeneous laterally complete modules”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, eds. S. Ayupov, V. Chilin, N. Ganikhodjaev, F. Mukhamedov, I. Rakhimov, IOP Publishing Ltd, 2016, 012002  crossref  isi  scopus
  • Владикавказский математический журнал
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