discipline 
Pure
Mathematics

subject 
Non commutative rings

lecturers 
István Ágoston,
József Pelikán 
credits 
2 
period 

curriculum 
Structure theory (primitive rings, Jacobson’s Density Theorem,
Jacobson radical, commutativity theorems). Central
simple algebras (tensor product of algebras, Noether–Skolem theorem, the Double Centralizer Theorem, the Brauer group, crossed products). Polynomial identities
(structure theorems, Kaplansky’s Theorem, Kurosh’ Problem, combinatorial results, quantitative
theory). Noetherian rings (Goldie’s Theorems and
generalizations, dimension theory). Artinian rings
and generalizations (semiperfect and perfect rings,
coherent rings, von Neumann regular rings). Morita theory (Morita
equivalence, Morita duality, Morita invariant ring properties). QuasiFrobenius rings (group algebras, symmetric algebras,
homological properties, QF1 and QF3 rings). Elements of representation
theory (hereditary algebras, Coxeter
transformations and Coxeter functors,
preprojective, preinjective
and regular representations, almost split sequences, the Brauer–Thrall
Conjectures, finite representation type). 
literature 
Herstein: Noncommutative
Rings Rowen: Ring Theory 
form of tuition 
Lecture 
mode of assessment 
written/oral
exam 