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Last update: T_KA (09.05.2013)
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Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (28.10.2019)
Students have to pass oral exam. |
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Last update: doc. Mgr. Pavel Růžička, Ph.D. (10.10.2017)
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 |
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Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (28.10.2019)
Students have to pass final oral exam. The requirements for the exam correspond to what has been done during lectures. |
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Last update: T_KA (09.05.2013)
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
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Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (17.05.2019)
Basics of general algebra. |