A binary operation-based representation of a lattice

Mourad Yettou; Abdelaziz Amroune; Lemnaouar Zedam

Kybernetika (2019)

  • Volume: 55, Issue: 2, page 252-272
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Yettou, Mourad, Amroune, Abdelaziz, and Zedam, Lemnaouar. "A binary operation-based representation of a lattice." Kybernetika 55.2 (2019): 252-272. <http://eudml.org/doc/294561>.

@article{Yettou2019,
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.},
author = {Yettou, Mourad, Amroune, Abdelaziz, Zedam, Lemnaouar},
journal = {Kybernetika},
keywords = {lattice; binary operation; neutral element; lattice representation},
language = {eng},
number = {2},
pages = {252-272},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A binary operation-based representation of a lattice},
url = {http://eudml.org/doc/294561},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Yettou, Mourad
AU - Amroune, Abdelaziz
AU - Zedam, Lemnaouar
TI - A binary operation-based representation of a lattice
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 2
SP - 252
EP - 272
AB - 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.
LA - eng
KW - lattice; binary operation; neutral element; lattice representation
UR - http://eudml.org/doc/294561
ER -

References

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