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Course, academic year 2019/2020
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Universal Algebra 2 - NMAG450
Title in English: Universální algebra 2
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017 to 2019
Semester: summer
E-Credits: 4
Hours per week, examination: summer s.:2/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
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
Annotation -
Last update: T_KA (14.05.2013)
Basic course in universal algebra.
Course completion requirements -
Last update: RNDr. Alexandr Kazda, Ph.D. (26.02.2018)

The sum of 4 best scores out of 5 written homeworks must be at least 60% of the maximum.

Additional homework will be assigned in case of failure, with a minimum of 60% marks for success.

It is necessary to fulfill this requirement before taking the exam.

Literature -
Last update: Michael Kompatscher, Ph.D. (21.02.2019)
  • C. Bergman: "Universal Algebra: Fundamentals and Selected Topics"
  • J. Jezek: "Universal Algebra"
  • L. Barto, M. Kozik: "Absorbing subalgebras, cyclic terms and the constraint satisfaction problem", Logical Methods in Computer Science 8/1:07 (2012), 1-26.
  • L. Barto, A. Krokhin, R. Willard: "Polymorphisms, and how to use them", Dagstuhl Follow-Ups. Vol. 7. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017.

Copies of Bergman's book are available at our library, while the other sources can be found on Libor Barto's website.

Further reading:

  • S. Burris, H. P. Sankappanavar: "A course in universal algebra." Springer-Verlag, 1981.
  • 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. (21.02.2019)

The final mark is determined by an oral exam.

Syllabus -
Last update: Michael Kompatscher, Ph.D. (21.02.2019)

This course offers a introduction to selected topics in universal algebra that are connected to the research interests of the algebra group. For the summer semester 2019 this includes:

  • Abelianness and basics of commutator theory
  • Term rewriting systems and the Knuth-Bendix algorithm
  • Absorption and its use in the study of Malcev conditions and CSPs

The lecture is taking place on Thursdays 09:00, in the seminar room of KA (K334KA). Once every two weeks the lecture is followed by an exercise class (Thursdays 10:40, seminar room of KA).

The language of both lecture and exercises is English.

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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