| topics | recommended reading | homework |
2.10. | Motivation. Algebra (signature, type). Homomorphism, isomorphism.
Ex.: (semi)lattice vs. semi(lattice) ordered set. Homomorphisms. |
Bergman 1.1, 1.2 | |
9.10. | Basic constructions - subalgebra, product.
Ex.: Homomorphisms, isomorphisms, products, subalgebras.
|
Bergman 1.3, 1.4 | |
16.10. | Quotients. HSP operators. Constructions and homomorphisms.
Ex.: Congruences of groups. Computing congruences and subalgebras. |
Bergman 1.5, (3.1, 3.5) | Homework 1 due 2 Nov 10:40 |
23.10. | Isomorphism theorems. Complete lattices.
Ex.: Join of congruences. |
Bergman 3.1, 2.3 | |
30.10. | Complete lattices, closure operators, Galois correspondeces.
Ex.: (Algebraic) complete lattices and (algebraic) closure operators |
Bergman 2.4, 2.5 | Homework 2 due 16 Nov 10:40 |
6.11. | Examples of Galois correspondeces. Direct decomposition.
Ex.: Direct decomposition |
Bergman 3.2 | |
13.11. | Subdirect decomposition.
Ex.: Subdirect decomposition |
Bergman 3.3 | |
20.11. | Terms, free algebras.
Ex.: Free algebras |
Bergman 4.3 | Homework 3 due 7 Dec 10:40 |
27.11. | Mod-Inv Galois correspondence, closed objects.
Ex.: Birkhoff's Theorem |
Bergman 4.4, 4.6 | |
4.12. | Clones.
Ex.: Clones of term operations |
Bergman 4.1 | Homework 4 due 21 Dec 10:40 |
11.12. | Pol-Inv Galois correspondence, closures of algebras.
Ex.: Pol, Inv |
Bergman 4.2 | |
18.12. | Relational clones.
Ex.: Pol-Inv |
| Homework 5 due 8 Jan 10:40 |
1.1. | ---------
Ex.: Compact clones, Boolean clones |
| |
8.1. | Mal'tsev conditions.
Ex.: Mal'tsev conditions |
Bergman 4.7 | |