Sumários
18ª aula
10 Maio 2023, 14:00 • Maria João Antunes Dias Gouveia
Free algebras over a set for a class of algebras; free algebras over a set in a class of algebras.
Read B & S, Chapter II, Section 10 till Definition 10.9 (not included).
16ª aula
3 Maio 2023, 14:00 • Maria João Antunes Dias Gouveia
The term algebras of a certain type over sets of variables. The universal mapping property. Resolution of some exercises.
15ª aula
26 Abril 2023, 14:00 • Maria João Antunes Dias Gouveia
Terms and identities of a certain type of algebras and over a certain set of variables. The definitions were introduced from examples of 3-element algebras defined by the students and some set of properties they identify to be satisfied by those algebras.
14ª aula
24 Abril 2023, 14:00 • Maria João Antunes Dias Gouveia
Proof of the following corollary of Birkhoff's Theorem: Every finite algebra is isomorphic to a subdirect product of a finite number of subdirectly irreducible finite algebras.
Theorem: For every variety generated by a finite set of finite lattice based algebras, its class of subdirectly irreducible algebras is, up to isomorphism, a finite set of finite algebras. (without proof)