Spring term 2025
Universal Algebra II (NMAG450)

Lecture: Tuesday 09:00 - 10:30, lecture room K2
Practicals: even weeks, Tuesday 10:40 - 12:10, lecture room K10C, run by Max Hadek

Lecture notes

Evaluation:
To obtain the credit (Zápočet) for the course you need to score at least 60% on 3 homework assignments.
The final grade will be determined by an oral exam, admission to the exam requires getting ''Zápočet'' first.

Date	Topics	Lecture notes	Exercises	Homework
17/02	Equational theories are fully invariant congruences, completeness theorem for equational logic.	Section 1.1
25/02	Term rewriting systems (finitely terminating/normal/convergent) Knuth-Bendix completion algorithm	Section 1.2, 1.3	1.3,1.4, (1.8),1.9
04/03	affine and Abelian algebras Fundamental theorem of Abelian algebras	Section 2.1, 2.2
11/03	The term conditions commutator, Examples (groups and lattices)	Section 2.3	EX2	HW1, due 25/03
18/03	Relational description of the commutator Characterization of congruence distributive varieties	Section 2.3, 2.4
25/03	finishing proof (CD varieties) Nilpotent algebras and the polynomial equivalence problem	Section 2.4, 2.5	EX3
01/04	Finitely based algebras Park's 4-element non-finitely based groupoid	Section 3
08/04	Park's conjecture McKenzies DPC result	Section 3.1	EX4	HW2, due 22/04
15/04	Jónsson' lemma, Proof outline of Baker's theorem CSPs over finite structures	Section 3.2, 4.1
22/04	the Pol-Inv Galois connection revisited Clone homomorphisms	Section 4.1, 4.2	EX5
29/04	Birkhoffs theorem for clones, minion homomorphisms Taylor's theorem	Section 4.2, 4.3	EX6
06/05	Proof of Taylor's theorem characterizations of finite Taylor algebras	Section 4.3.	EX6	HW3
13/05	Dean's sports day
20/05	finite Taylor implies 6-ary Siggers	Section 4.4.

Consultation:
If you have questions on the material, do not hesitate to ask (either in person or via e-mail)! I have no official office hours, but personal meetings can be arranged. Please make also use of the exercise classes to discuss your questions.