discipline 
Pure
Mathematics

subject 
Universal Algebra I.

lecturers 
Emil Kiss, Csaba Szabó 
credits 
2 
period 

curriculum 
Introduction. Similarity
type, algebra, clone, term, polynomial. Subalgebra,
homomorphism, direct product, identity, variety, Birkhoff's
theorems. Congruence lattice, subalgebra lattice, Mal'tsev's Lemma. Subdirect decomposition,
subdirectly irreducible algebras. Quackenbush's Conjecture. Graph algebras. Mal'tsev conditions, the
characterization of congruence permutable, congruence distributive and
congruence modular varieties. Jónsson's Lemma,
Fleischer's Theorem. Baker's finite basis theorem. Completeness questions,
primal and functionally complete algebras and their characterizations
(FosterPixley, BakerPixley,
Commutator Theory. Abelian
algebras, centrality, the properties of the commutator
in modular varieties. Gumm's shifting lemma, the
semantic definition of the commutator, the proof of
the commutator properties. Difference term, the Fundamental
Theorem of Abelian Algebras (TaylorHerrmann). The
structure of Abelian congruences,
the module associated with them. Gumm's
characterization ofcentrality. Generalized Jónsson Theorem. 
literature 
BurrisSankappanavar: A
course in Universal Algebra FreeseMcKenzie: Commutator
theory for congruence modular varieties 
form of tuition 
Lecture 
mode of assessment 
written/oral
exam 