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, NoetherSkolem 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). Quasi-Frobenius rings (group algebras, symmetric algebras, homological properties, QF-1 and QF-3 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