Browsing by Author "Supervisor: Yettou, Mourad"

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    Algebraic derivations on a lattice (Dérivations algébriques dans un treillis)
    (UNIVERSITY of M'SILA, 2022-06-10) Delloum, Sabrin; Supervisor: Yettou, Mourad
    In the memory, we first have recalled the necessary basic concepts and properties of binary relations on a set and partially ordered sets. Then, we have given general information on lattices and algebraic properties of some lattice classes. Also, we have provided the notion of an algebraic derivation on a lattice and we have discussed some related properties. Further, we have analyzed some classes of derivations on a lattice like principal and isotone derivations. Moreover, we have recalled the notion of a fixed point of a derivation on a lattice and we have presented the algebraic structure of the set of these fixed points.
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    On Boolean Lattices (Sur les Treillis Booléens)
    (University of M'sila, 2023-06-10) Belkaaloul, Rihab; Tayabi, Siham; Supervisor: Yettou, Mourad
    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.