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Fundam. Prikl. Mat., 2008, Volume 14, Issue 5, Pages 85–92 (Mi fpm1142)  

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

On quasiorder lattices and topology lattices of algebras

A. V. Kartashova

Volgograd State Pedagogical University

Abstract: In this paper, it is shown that the dual $\widetilde{\mathrm{Qord}} \mathfrak A$ of the quasiorder lattice of any algebra $\mathfrak A$ is isomorphic to a sublattice of the topology lattice $\Im(\mathfrak A)$. Further, if $\mathfrak A$ is a finite algebra, then $\widetilde{\mathrm{Qord}} \mathfrak A\cong\Im(\mathfrak A)$. We give a sufficient condition for the lattices $\widetilde{\mathrm{Con}} \mathfrak A$, $\widetilde{\mathrm{Qord}} \mathfrak A$, and $\Im(\mathfrak A)$ to be pairwise isomorphic. These results are applied to investigate topology lattices and quasiorder lattices of unary algebras.

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English version:
Journal of Mathematical Sciences (New York), 2009, 163:6, 682–687

Bibliographic databases:

UDC: 512.57

Citation: A. V. Kartashova, “On quasiorder lattices and topology lattices of algebras”, Fundam. Prikl. Mat., 14:5 (2008), 85–92; J. Math. Sci., 163:6 (2009), 682–687

Citation in format AMSBIB
\Bibitem{Kar08}
\by A.~V.~Kartashova
\paper On quasiorder lattices and topology lattices of algebras
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 5
\pages 85--92
\mathnet{http://mi.mathnet.ru/fpm1142}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2533579}
\elib{http://elibrary.ru/item.asp?id=12174987}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 163
\issue 6
\pages 682--687
\crossref{https://doi.org/10.1007/s10958-009-9704-8}
\elib{http://elibrary.ru/item.asp?id=15302833}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-73249124318}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Kartashova, “O reshetkakh kongruentsii i topologii unarnykh algebr”, Chebyshevskii sb., 12:2 (2011), 27–33  mathnet  mathscinet
  • Фундаментальная и прикладная математика
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