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Algebra and Discrete Mathematics, 2017, Volume 24, Issue 2, Pages 274–296 (Mi adm633)  
RESEARCH ARTICLE

Lattice rings: an interpretation of $L$-fuzzy rings as habitual algebraic structures

Leonid A. Kurdachenkoa, Igor Ya. Subbotinb, Viktoriia S. Yashchuka

a Department of Algebra, Oles Honchar Dnipro National University, 72 Gagarin Av., Dnipro 49010, Ukraine
b Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, LA, CA 90045, USA
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Abstract: In this paper, we introduce some algebraic structure associated with rings and lattices. It appeared as the result of our new approach to the fuzzy rings and $L$-fuzzy rings 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: ring, lattice, distributive lattice, fuzzy ring, homomorphism.
Received: 14.11.2016
Bibliographic databases:
Document Type: Article
MSC: 20M10, 06D99, 16W99
Language: English
Citation: 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
Citation in format AMSBIB
\Bibitem{KurSubYas17}
\by Leonid~A.~Kurdachenko, Igor~Ya.~Subbotin, Viktoriia~S.~Yashchuk
\paper Lattice rings: an interpretation of $L$-fuzzy rings as habitual algebraic structures
\jour Algebra Discrete Math.
\yr 2017
\vol 24
\issue 2
\pages 274--296
\mathnet{http://mi.mathnet.ru/adm633}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000423934100008}
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