ARCHIV 20/21 letni semestr
[Zpet]
UNIVERSAL ALGEBRA 2 (NMAG450)
Lecture: Mon 10:40 - 12:10 zoom
Practicals: Mon 12:20 - 13:50 zoom, even weeks
Grading:
- Practicals ("Z: Zapocet"): homeworks (60% from 3 best scores out of 4 homeworks)
- Lecture ("Zk: Zkouska"): written test + possible oral examination
Link to material only for NMAG450 students" (e.g. lecture recordings). The username and password was sent to you by email.
Homework
- Please prepare in PDF format. Latex or handwritting+Adobe Scan highly recommended.
- Submitting: send by email
- I will add comments to the PDF and record your mark to SIS
Literature:
 
| topics | recommended reading | lecture notes practicals | homework |
1.3. | Abelian and affine algebras, fundamental theorem. |
Bergman 7.3, MK 2.1, 2.2 | lecture 1 | |
8.3. | Relational desciption of Abelian algebras. Centralizing relation in UA vs. group theory.
Pr.: Abelian and non-Abelian algebras.
|
Bergman 7.4, MK 2.3 | lecture 2 practical 1 |
homework 1 due 22 Mar 9:00 |
15.3. | Equational theories, completness theorem for equational logic. |
Jezek 13, MK 1.1,1.2 | lecture 3 | |
22.3. | Reduction order, critical pairs, Knuth-Bendix algorithm.
Pr.: Convergent rewriting systems. |
Jezek 13, MK 1.3 | lecture 4 practical 2 | homework 2 due 12 Apr 9:00 |
29.3. | Finitely based varieties. Non-finitely based example.
|
Bergman 5.4., MK 3.0 | lecture 5 | |
5.4. | ---
|
| | |
12.4. | McKenzie's DPC (definable principal congruences) result. |
Bergman 5.5., MK 3.1 | lecture 6 | |
19.4. | Constraint satisfaction problems over fixed templates.
Pr.: DPC. CSPs. |
MK 4.1, BKW | lecture 7 practical 3 | |
26.4. | Clone homomorphisms. minion homomorphism |
MK 4.2, BKW | lecture 8 | homework 3 due 10 May 9:00 |
3.5. | Taylor algebras, Taylor's theorem.
Pr.: HSP vs HS |
MK 4.3 | lecture 9 practical 4 | |
10.5. | Absorption theorem |
BK | lecture 10 | |
17.5. | Finite Taylor abelian algebras are affine
Pr.: Absorption, linked relations |
BK | lecture 11 practical 5 | homework 4 due 31 May 9:00 |
24.5. | Loop lemma |
BK | lecture 12 | |
31.5. | Minimal Taylor clones
Pr.: Loop lemma |
| ISMVL talk practical 6 | |
 
 
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