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LINEARNI ALGEBRA A GEOMETRIE 2 (NMAG102)
Stranka kurzu
UNIVERSAL ALGEBRA 2 (NMAG450)
Lecture: Thursday 15:40  17:10 KA
Tutorial: Thursday 17:20  18:05 KA (instructor: Jakub Oprsal)
LECTURES
 27.2. Malt'sev conditions for congruence permutability and congruence distributivity.
 6.3. Interpretation, interpretability lattice. Thm: Idempotent variety V is not interpretable into sets iff V has a Taylor term.
 13.3. Equational theory. Thm: Id(Mod(E)) = eq.theory generated by E. Equational completeness theorem (semantic consequence=syntactic consequence).
 20.3. Rewriting systems. Converegent digraphs. Thm: Convergent = locally confluent + finitely terminating.
Reduction order. The most general unifier, critical pair. KnuthBendix algorithm.
 27.3. KnuthBendix ordering.
 3.4. Finile based variety/algebra. Thm: finitely based = finitely axiomatizable. Thm: depends only on the clone of the algebra.
Thm: F.B. <=> basis of nvariable identites for some n. Example of a finite algebra which is not finitely based.
 10.4. Definable principal congruences (DPC). Thm: DPC => principal congruence can be defined by "conservative" formula.
Thm: V has DPC + finitely many SIs, all finite => V is finitely based.
 17.4. Affine algebra (=polynomially equivalent to a module). Abelian algebra. Thm: affine <=> Maltsev and abelian.
Thm: If Maltsev then abelian <=> affine <=> the Maltsev is central.
 24.4. C(alpha, beta delta): alpha centralizes beta modulo delta. Thm: It has the expected meaning in groups. Commutator.
 1.5. 
 8.5. 
 15.5. Tame congruence theory: Neighborhood, miminal set, uniformity and density. Classification of minimal algebras.
 22.5. 
LITERATURE
SEMINAR K PROBLEMU CSP (NALG118)
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