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Sibirsk. Mat. Zh., 2001, Volume 42, Number 3, Pages 491–506 (Mi smj1438)  

This article is cited in 3 scientific papers (total in 3 papers)

On maximal chains in the lattice of module topologies

V. I. Arnautov, K. M. Filippov

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

Abstract: Let $(R,\tau_R)$ be a topological ring and $ _RM$, a left unitary $R$-module. The set $L(M)$ of all $(R,\tau_R)$-module topologies on $ _RM$ is a complete modular lattice. A topology $\tau\in L(M)$ is $n$-premaximal if in $L(M)$ there exists an inclusion-maximal chain $\tau_>\tau_1>…>\tau_n$ such that $\tau_0$ is the largest element in $L(M)$ and $\tau_n=\tau$. Section 1 contains conditions for existence of 1-premaximal Hausdorff topologies on $ _RM$. Section 2 contains a description of all $n$-premaximal topologies in the case when $(R,\tau_R)$ is a topological skew field whose topology is determined by a real absolute value.

Full text: PDF file (276 kB)

English version:
Siberian Mathematical Journal, 2001, 42:3, 415–427

Bibliographic databases:

UDC: 512.556.5
Received: 13.05.1998

Citation: V. I. Arnautov, K. M. Filippov, “On maximal chains in the lattice of module topologies”, Sibirsk. Mat. Zh., 42:3 (2001), 491–506; Siberian Math. J., 42:3 (2001), 415–427

Citation in format AMSBIB
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\by V.~I.~Arnautov, K.~M.~Filippov
\paper On maximal chains in the lattice of module topologies
\jour Sibirsk. Mat. Zh.
\yr 2001
\vol 42
\issue 3
\pages 491--506
\mathnet{http://mi.mathnet.ru/smj1438}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1852230}
\zmath{https://zbmath.org/?q=an:1020.16033}
\transl
\jour Siberian Math. J.
\yr 2001
\vol 42
\issue 3
\pages 415--427
\crossref{https://doi.org/10.1023/A:1010469606306}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000169277100001}


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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. I. Arnautov, K. M. Filippov, “On Prebox Module Topologies”, Math. Notes, 74:1 (2003), 12–17  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Arnautov V., Filippov K., “On group topologies on an abelian group preceding one another”, Computational Commutative and Non-Commutative Algebraic Geometry, NATO Science Series, Sub-Series III: Computer and Systems Sciences, 196, 2005, 251–267  mathscinet  zmath  isi
    3. V. I. Arnautov, “On coverings in the lattice of all group topologies of arbitrary Abelian groups”, Siberian Math. J., 47:5 (2006), 787–796  mathnet  crossref  mathscinet  zmath  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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