Libor Barto Studenti

Libor Barto

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UNIVERSAL ALGEBRA 2 (NMAG450)

Lecture: Tue 10:40 - 12:10 K12
Practicals run by Michael Kompatscher: Tue 12:20 - 13:50 K7, even 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)

topics recommended reading lecture notes
practicals homework

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

21.2. 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 7 Mar 10:40

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

7.3. Reduction order, critical pairs, Knuth-Bendix algorithm.
Pr.: Convergent rewriting systems. MK 1.3, Jezek 13 lecture 4
practical 2 homework 2
due 21 Mar 10:40

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

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

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

4.4. Clone homomorphisms. minion homomorphism
Pr.: ??? HSP vs HS MK 4.2, BKW lecture 8
practical 4 homework 3
due 18 Apr 10:40

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

18.4. Absorption theorem
Pr.: Absorption, linked relations BK lecture 10
practical 5 homework 4
due 2 May 10:40

25.4. Finite Taylor abelian algebras are affine
BK lecture 11

2.5. Loop lemma
Pr.: Loop lemma BK lecture 12
practical 6

9.5. ???

16.5. ???
Pr.: ???

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