M8820 Ordered sets and lattices

Faculty of Science
Spring 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
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.
The course is also listed under the following terms Spring 2001.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2002/M8820