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Introduction to the lattice theory: structure and basic properties of distributive and modular lattices, structure of congruences
of lattices, free lattices, lattice varieties.
Last update: T_KA (09.05.2013)
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Students have to pass oral exam. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.10.2019)
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1. Gratzer, G. General Lattice Theory (2nd ed.), Birkhauser Verlag, Basel, 1998.
2. Nation, J. B., Notes on Lattice Theory. Cambridge studies in advanced mathematics, 1998. Online: https://pdfs.semanticscholar.org/a16b/e5f1b0f120d0eacc1615ef5492fc2d9a32c3.pdf Last update: Růžička Pavel, doc. Mgr., Ph.D. (10.10.2017)
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Students have to pass final oral exam. The requirements for the exam correspond to what has been done during lectures. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.10.2019)
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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
Last update: T_KA (09.05.2013)
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Basics of general algebra. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (17.05.2019)
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