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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

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

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.

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Bibliographic databases:
MSC: 20M10, 06D99, 20M99
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} 

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