Belkaaloul, RihabTayabi, SihamSupervisor: Yettou, Mourad2023-07-022023-07-022023-06-10http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/39864In 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.enOrdered set, lattices, ideals, filters, sub-lattice, lattice morphism, Boolean lattice.Thesis