On Boolean Lattices (Sur les Treillis Booléens)
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Date
2023-06-10
Journal Title
Journal ISSN
Volume Title
Publisher
University of M'sila
Abstract
In this thesis, we present the notion of Boolean lattices and their properties. To that end, we
recall the necessary concepts and properties of binary relations, partially orders and ordered
sets. Moreover, we present the necessary concepts and properties of lattices, ideals, filters,
sub-lattices and lattice morphisms. Further, we focus our attention on the algebraic structure
of Boolean lattices and their characterizations. Finally, we give some methods to solve linear
equations and inequalities on a Boolean lattice.
Description
Keywords
Ordered set, lattices, ideals, filters, sub-lattice, lattice morphism, Boolean lattice.