Geodesic
A binary operation-based representation of a lattice
Kybernetika, Tome 55 (2019) no. 2, pp. 252-272.

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In this paper, we study and characterize some properties of a given binary operation on a lattice. More specifically, we show necessary and sufficient conditions under which a binary operation on a lattice coincides with its meet (resp. its join) operation. Importantly, we construct two new posets based on a given binary operation on a lattice and investigate some cases that these two posets have a lattice structure. Moreover, we provide some representations of a given lattice based on these new constructed lattices.
DOI : 10.14736/kyb-2019-2-0252
Classification : 06B05, 06B15
Keywords: lattice; binary operation; neutral element; lattice representation 
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Yettou, Mourad; Amroune, Abdelaziz; Zedam, Lemnaouar. A binary operation-based representation of a lattice. Kybernetika, Tome 55 (2019) no. 2, pp. 252-272. doi : 10.14736/kyb-2019-2-0252. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-2-0252/

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