Kybernetika 55 no. 2, 252-272, 2019

A binary operation-based representation of a lattice

Mourad Yettou, Abdelaziz Amroune and Lemnaouar ZedamDOI: 10.14736/kyb-2019-2-0252

Abstract:

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.

Keywords:

binary operation, lattice, neutral element, lattice representation

Classification:

06B05, 06B15

paper.pdf

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