Syllabus
Basic properties of lattices: lattices as ordered sets, algebraic concept, homomorphisms, congruences and ideals, join-irreducible elements
Distributive lattices: characterization, free distributive lattices, congruences of distributive lattices, topological representation
Congruences and ideals: weak projectivity and perspectivity, distributive, standard and neutral elements and ideals, congruences of a cartesian product, modular and weakly modular lattices, distributivity of the congruence lattice of a lattice
Modular and semimodular lattices: characterization, Kurosh-Ore theorem, congruences in modular lattices, von Neumann theorem, Birghoff theorem, semimodular lattices, Jordan-Hölder theorem, geometric lattices, partition lattices, complemented modular lattices and projective geometries
Annotation
Introduction to the lattice theory: structure and basic properties of distributive and modular lattices, structure of congruences of lattices, free lattices, lattice varieties.