Libor Barto
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ARCHIV 20/21 zimni semestr

[Zpet]

UNIVERSAL ALGEBRA (NMAG405)

Lecture: Thr 9:00 - 10:30 zoom
Practicals run by William DeMeo: Thr 10:40 - 12:10 zoom (the link contains material for/from practicals)

• Practicals ("Z: Zapocet"): homeworks (60% from 4 best scores out of 5 homeworks)
• Lecture ("Zk: Zkouska"): 15% homeworks, 85% written test + possible oral examination

Literature:

Link to material only for NMAG405 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.

 topics (future topics may change) recommended reading lecture notes homework 8.10. Motivation. Algebra (signature, type). Examples. Pr.: Lattices vs. lattice ordered sets Bergman 1.1, 1.2 lecture 1 15.10. Lattices, complete lattices, closure operators. Pr.: Distributive and modular lattices. The lattice of equivalence relations. Bergman 2.1, 2.2, 2.3 lecture 2 22.10. Algebraic lattices and closure operators. Galois correspondences. Pr.: Complete lattices, closure operators, Galois correspondences. Bergman 2.4, 2.5 lecture 3 Homework 1 due 5 Nov 29.10. Subalgebras, products, quotients. Pr.: Subalgebras, congruences. Bergman 1.3, 1.4, 1.5 lecture 4 corrected (lower quality) 5.11. H,S,P operators, variety. Homomorphisms. Pr.: Homomorphisms. Finite algebras generate locally finite varieties. Bergman 1.1, 1.3, 3.1, 3.5 lecture 5 Homework 2 due 19 Nov 12.11. Direct and subdirect decomposition Pr.: Direct and subdirect decomposition. Bergman 3.2, 3.3 lecture 6 19.11. Subdirect decomoposition, SIs in congruence distributive vaieties Pr.: SIs in monounary algebras. Bergman 3.4, 3.5, (5.2) lecture 7 Homework 3 due 3 Dec 26.11. Terms, identities, free algebras. Pr.: Free algebras. Bergman 4.3, 4.4 lecture 8 3.12. The syntax-semantics Galois correspondence, Birkhoff's theorem. Pr.: Equational bases. Bergman 4.4, (4.6) lecture 9 Homework 4 due 17 Dec 10.12. Clones. Free algebras as clones of term operations. Pr.: Clones. Bergman 4.1 lecture 10 17.12. The operations-relations Galois correspondence. Pr.: Algebraic and relational clones. Bergman 4.2 lecture 11 Homework 5 due 7 Jan 7.1. Mal'cev conditions: Mal'cev, majority. Mal'cev conditions Bergman 4.7 (part) lecture 12

Run by Antoine Mottet: Fri 9:00 Zoom

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