PřF:M8820 Ordered sets and lattices - Course Information
M8820 Ordered sets and lattices
Faculty of ScienceSpring 2002
- Extent and Intensity
- 2/0/0. 4 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Josef Niederle, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Josef Niederle, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Josef Niederle, CSc. - Prerequisites
- M4160 Algebra II && M4150 Set theory
Basic courses in set theory, discrete mathematics and algebra. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Complete lattices
Complete partially ordered sets
Fixpoints
Lattices as algebras
Modular and distributive lattices
Boolean lattices
Ideals and filters
Representation of distributive lattices - Syllabus
- Complete lattices: down-sets and up-sets, topped intersection structures, closure operators, Dedekind-MacNeille completion, Galois connection, concept lattices
- Complete partially ordered sets: algebraic intersection structures, algebraic closure operators, algebraic lattices, domains
- Fixpoints: fixpoint theorems
- Lattices as algebras: sublattices, products, homomorphisms
- Modular and distributive lattices: the M_3-N_5 theorem
- Boolean lattices
- Ideals and filters: prime ideals, maximal ideals
- Representation of distributive lattices: duality between finite distributive lattices and finite ordered sets, representation by lattices of sets, duality
- Literature
- DAVEY, B. A. and H. A. PRIESTLEY. Introduction to Lattices and Order. Cambridge: Cambridge University Press, 1990, 248 pp. Cambridge Mathematical Textbooks. ISBN 0-521-36766-2. info
- Language of instruction
- Czech
- Further Comments
- The course is taught once in two years.
The course is taught: every week.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/sci/spring2002/M8820