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Course, academic year 2023/2024
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Universal Algebra 2 - NMAG450
Title: Universální algebra 2
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 4
Hours per week, examination: summer s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. Mgr. Libor Barto, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Incompatibility : NALG104
Interchangeability : NALG104
Is interchangeable with: NALG104
Annotation -
Last update: T_KA (14.05.2013)
Basic course in universal algebra.
Course completion requirements -
Last update: Michael Kompatscher, Ph.D. (14.02.2022)

It is necessary to score at least 60% on 3 homework assignments to obtain "Zápočet" and be admitted to the exam.

Literature -
Last update: Michael Kompatscher, Ph.D. (14.02.2022)

There will be lecture notes for the course. Several (but not all) of the topics are also discussed in the book

  • C. Bergman: "Universal Algebra: Fundamentals and Selected Topics",

which can be found in our library.

Various sources for further reading:

  • S. Burris, H. P. Sankappanavar: "A course in universal algebra." Springer-Verlag, 1981.
  • L. Barto, A. Krokhin, R. Willard: "Polymorphisms, and how to use them", Dagstuhl Follow-Ups. Vol. 7. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017.
  • L. Barto, M. Kozik: "Absorbing subalgebras, cyclic terms and the constraint satisfaction problem", Logical Methods in Computer Science 8/1:07 (2012), 1-26.
  • J. Jezek: "Universal Algebra"
  • R. McKenzie, G. McNulty, W. Taylor: "Algebras, Lattices, Varieties", vol. 1. Wadsworth and Brooks/Cole, 1987.
  • R. Freese, R. McKenzie: "Commutator theory for congruence modular varieties", LMS Lecture Notes, Vol. 125, Cambridge, 1987.

Requirements to the exam -
Last update: Michael Kompatscher, Ph.D. (14.02.2022)

The final mark is determined by an oral exam.

Syllabus -
Last update: Michael Kompatscher, Ph.D. (14.02.2022)

This course offers an introduction to selected topics in universal algebra that are connected to the research interests of the algebra group. In summer semester 2022 this includes:

  • Term rewriting systems and the Knuth-Bendix algorithm
  • Abelianness and basics of commutator theory
  • Finitely based algebras
  • The study of Maltsev conditions (Taylor terms) and their relevance to CSPs
Entry requirements -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (17.05.2019)

Knowledge on level of the course Universal Algebra 1.

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