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Libor Barto

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UNIVERSAL ALGEBRA 2 (NMAG450)

Lecture: Wed 9:00 - 10:30 K4
Practicals run by Max Hadek: Wed 10:40 - 12:10 K4, even semester weeks (odd calendar weeks)

Grading:

Practicals ("Z: Zapocet"): homeworks (60% from 3 best scores out of 4 homeworks)
Lecture ("Zk: Zkouska"): written test + oral examination

Literature:

(MK) Michael Kompatscher: Lecture notes
Clifford Bergman: Universal Algebra: Fundamentals and Selected Topics
Jaroslav Jezek: Universal Algebra
(BKW) Barto, Krokhin, Willard: Polymorphisms, and how to use them .
(BK) Barto, Kozik: Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem
Burris, Sankappanavar: A Course in Universal Algebra (an alternative source of examples and exercises)

Lecture recordings from 2020/21 only for NMAG450 students" . The username and password was sent to you by email.

topics recommended reading lecture notes
practicals homework

18.2. Abelian and affine algebras, fundamental theorem. MK 2.1, 2.2, Bergman 7.3 lecture 1

25.2. Relational desciption of Abelian algebras. Centralizing relation in UA vs. group theory.
Pr.: Abelian and non-Abelian algebras. MK 2.3, Bergman 7.4 lecture 2
practical 1 homework 1
due 11 Mar 10:40

4.3. Equational theories, completness theorem for equational logic. MK 1.1,1.2, Jezek 13 lecture 3

11.3. Reduction order, critical pairs, Knuth-Bendix algorithm.
Pr.: Convergent rewriting systems. MK 1.3, Jezek 13 lecture 4
practical 2 homework 2
due 25 Mar 10:40

18.3. Finitely based varieties. Non-finitely based example. MK 3.0, Bergman 5.4. lecture 5

25.3. McKenzie's DPC (definable principal congruences) result.
Pr.: DPC. MK 3.1, Bergman 5.5. lecture 6
practical 3

1.4. Constraint satisfaction problems over fixed templates. MK 4.1, BKW lecture 7

8.4. Clone homomorphisms. minion homomorphism
Pr.: HSP vs HS MK 4.2, BKW lecture 8
practical 4 homework 3
due 22 Apr 10:40

15.4. Taylor algebras, Taylor's theorem. MK 4.3 lecture 9

22.4. Absorption theorem
Pr.: Absorption, linked relations BK lecture 10
practical 5 homework 4
due 6 May 10:40

29.4. Finite Taylor abelian algebras are affine
BK lecture 11

6.5. Loop lemma
Pr.: Absorption, linked relations BK lecture 12
practical 6

13.5. ----

20.5. Few subpowers (?)
Pr.: Few subpowers
lecture 13
practical 7

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