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Algebra Discrete Math., 2015, Volume 20, Issue 1, Pages 126–141 (Mi adm535)  

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

RESEARCH ARTICLE

Lattice groups

L. A. Kurdachenkoa, V. S. Yashchuka, I. Ya. Subbotinb

a Department of Algebra, Oles Honchar Dnipropetrovsk National University
b Department of Mathematics and Natural Sciences, National University

Abstract: In this paper, we introduce some algebraic structure associated with groups and lattices. This structure is a semigroup and it appeared as the result of our new approach to the fuzzy groups and $L$-fuzzy groups where $L$ is a lattice. This approach allows us to employ more convenient language of algebraic structures instead of currently accepted language of functions.

Keywords: group, lattice, distributive lattice, fuzzy group, semigroup.

Full text: PDF file (355 kB)
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Bibliographic databases:
MSC: 20M10, 06D99, 20M99
Received: 02.04.2015
Revised: 02.04.2015
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Citation: L. A. Kurdachenko, V. S. Yashchuk, I. Ya. Subbotin, “Lattice groups”, Algebra Discrete Math., 20:1 (2015), 126–141

Citation in format AMSBIB
\Bibitem{KurYasSub15}
\by L.~A.~Kurdachenko, V.~S.~Yashchuk, I.~Ya.~Subbotin
\paper Lattice groups
\jour Algebra Discrete Math.
\yr 2015
\vol 20
\issue 1
\pages 126--141
\mathnet{http://mi.mathnet.ru/adm535}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431955}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000378728700010}


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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. Leonid A. Kurdachenko, Igor Ya. Subbotin, Viktoriia S. Yashchuk, “Lattice rings: an interpretation of $L$-fuzzy rings as habitual algebraic structures”, Algebra Discrete Math., 24:2 (2017), 274–296  mathnet
  • Algebra and Discrete Mathematics
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