On Boolean Lattices (Sur les Treillis Booléens) - Belkaaloul, Rihab; Tayabi, Siham; Supervisor: Yettou, Mourad (University of M'sila, 2023)
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.
Keywords: Ordered set, lattices, ideals, filters, sub-lattice, lattice morphism, Boolean lattice.