Teaching 2018/19:

Universal Algebra II (NMAG450)

The course will roughly follow Libor Barto's lecture from 17/18.

Lecture: Thurday 9:00 - 10:30 Seminar room of KA
Exercises: Thurday 10:40 - 12:10 Seminar room of KA (only odd semester weeks = even calendar weeks)

Grading:
Exercises: homeworks (60% from 3 best scores out of 4 homeworks)
Lecture: oral examination (appointment by mail: michael@logic.at).
next available dates 27/05-07/06; 17/06-20/06; 04/07-

Literature:
Date Topics Recommended reading Exercises Homework
28/02Abelian and affine algebras, Fundamental theorem. Bergman 7.3 Ex. 1
07/03Checking identities, Relational description of Abelianness;
Centralizer relation (in general and in groups)
Bergman 7.4
14/03Properties of the commutator
Characterization of CD varieties
Bergman 7.4 Ex. 2 HW 1
due 28/03
21/03Equational theories, fully invariant congruences;
completeness theorem for equational logic.
Bergman 4.6
Jezek 13
28/03Reduction order, critical pairs
Knuth-Bendix algorithm
Jezek 13Ex. 3
04/04Examples of finitely based and non finitely based algebrasBergman 5.4HW 2
due 25/04
11/04 McKenzie's result on definable principal congruencesBergman 5.5Ex. 4
18/04Constraint satisfaction problems over finite templates
Pol-Inv revisited
BKW
25/04(h1-)clone homomorphisms
Taylor terms
BKWEx. 5HW 3
due 09/05
02/05Taylor's theoremBergman 8.4.
09/05Smooth digraphs, algebraic length 1,absorptionBK
16/05Absorption, transitive termsBKEx. 6HW 4
23/05Absorption theorem, LLL (loop lemma 'light', for linked digraphs)BK


Exercises in Universal Algebra I (NMAG405)

see David Stanovsky's website.