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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 2, Pages 185–193 (Mi timm234)  

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

On finite critical lattices

O. E. Perminova

Ural State University

Abstract: Critical lattices are considered, i.e., lattices without nontrivial endomorphisms and not containing nontrivial proper sublattices without nontrivial endomorphisms. It is proved that there exist $n$-element critical sublattices for any $n\ge21$.

Keywords: lattice, sublattice, endomorphism, critical lattice

Full text: PDF file (169 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 267, suppl. 1, S192–S200

Bibliographic databases:

UDC: 512.562
Received: 12.02.2009

Citation: O. E. Perminova, “On finite critical lattices”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 185–193; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S192–S200

Citation in format AMSBIB
\Bibitem{Per09}
\by O.~E.~Perminova
\paper On finite critical lattices
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 2
\pages 185--193
\mathnet{http://mi.mathnet.ru/timm234}
\elib{http://elibrary.ru/item.asp?id=12878780}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S192--S200
\crossref{https://doi.org/10.1134/S0081543809070177}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000274041900017}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. O. E. Perminova, “O konechnykh kriticheskikh reshetkakh. II”, Tr. IMM UrO RAN, 17, no. 4, 2011, 278–292  mathnet  elib
    2. O. E. Perminova, “O funktsii rosta konechnykh zhestkikh reshetok”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 4:2 (2011), 124–133  mathnet
    3. O. E. Perminova, “Neaksiomatiziruemost klassa kriticheskikh reshetok”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:4 (2012), 66–78  mathnet
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