Sumários
13ª aula
19 Abril 2023, 14:00 • Maria João Antunes Dias Gouveia
The variety of (bounded) distributive lattices is the variety generated by the two-element lattice.
Leitura/reading: B&S, 58-59; suggestion: solve exercises 3 and 4 on page 60.
12ª aula
17 Abril 2023, 14:00 • Maria João Antunes Dias Gouveia
Subdirect Representation Theorem (Birkhoff).
11ª aula
3 Abril 2023, 14:00 • Maria João Antunes Dias Gouveia
Subdirect embeddings and subdirectories products. Subdirectly irreducible algebras.
The existence of maximal congruences on an algebra with respect to separate elements (i.e. to not contain some pair of elements).
Leitura/reading: B&S, 54-58 (since Definition 7.11)
Easter Vacation: 06-04 to 12-04
10º aula
29 Março 2023, 14:00 • Maria João Antunes Dias Gouveia
The lattice of equivalence relations on a set and the lattice of the congruence relations on an algebra.
Leitura/reading: B&S, 35-38 (notice that we have not defined yet algebraic lattice, for now what matters is that we get a lattice structure)
Bergman book, pages 13-19 (try to prove Theorem 1.25 and pick up some of the exercises and solve them)