| Course title | Theory of Lattices |
|---|---|
| Course code | KAG/PGSTZ |
| Organizational form of instruction | Lecture |
| Level of course | Doctoral |
| Year of study | not specified |
| Semester | Winter and summer |
| Number of ECTS credits | 5 |
| Language of instruction | Czech, English |
| Status of course | unspecified |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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1. Lattices as posets and as algebraic structures. 2. Complete lattices: Closure operators, closed set systems, algebraic closure oparators, compact elements. 3. The Dedekind McNeill hull of a poset, completions of posets. 4. Congruence properties of lattices: Ideals and filters in lattices, the Hashimoto theorems. 5. Modular lattices, their representation, covering conditions, the Jordan-Hölder condition, fundamentals of geometric lattices, the Kurosh-Ore theorem. 6. Distributive lattices: Representation theorems, lattices with pseudocomplements, distributive, standard and neutral elements. 7. Boolean algebras: Representation, the Stone spaces. 8. Free lattices and their properties.
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| Learning activities and teaching methods |
| Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming) |
| Learning outcomes |
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Deepen knowledges from lattice theory.
Getting deep knowledges from posets and lattices. |
| Prerequisites |
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unspecified
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| Assessment methods and criteria |
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Oral exam, Written exam
Credit: active participation in seminars. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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