Algebraic Linear Differential Equations on Boolean Lattices
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Date
2025-06-10
Journal Title
Journal ISSN
Volume Title
Publisher
Mohamed Boudiaf University of M'sila
Abstract
In this memory, we have focused on studying the concept of algebraic linear
differential equations on Boolean lattices. To that end, we have organized our thesis
into three chapters. We have devoted the first chapter for recalling basic concepts and
properties of lattices. Moreover, we have presented some classes of lattices,
distributive, modular and Boolean lattices. In chapter 2, we have focused our study on
the concepts of derivations and integrations on lattices, and their properties. The third
chapter is the main goal of this thesis, where we provided the newly notion of algebraic
linear differential equations on Boolean lattices. Further, we have established the
necessary and sufficient conditions to sole those differential equations. In addition, we
have used Python Programs for solving those linear differential equations.
Description
Keywords
Poset, lattice, Boolean lattice, derivation, integration, algebraic linear differential equation