discipline 
Pure
Mathematics

subject 
Homological Algebra

lecturers 
István Ágoston, József Pelikán 
credits 
2 
period 

curriculum 
The Hom and tensor functors (projective,
injective and flat modules). Homological properties of special classes of
rings (semisimple, von Neumann regular, hereditary, quasiFrobenius rings).
Homologies of complexes: homology groups, projective and injective
resolutions. Derived functors (construction of Ext and Tor, basic
properties). Exact sequences and the Ext functor (Yoneda product, Ext
algebras). Homological dimensions (projective and injective dimension, global
dimension, the Hilbert Syzygy Theorem, dominant dimension, Auslander
algebras, finitistic dimension, the Finitistic Dimension Conjecture).
Homological methods in the representation theory of algebras (almost split
sequences, the Auslander–Reiten quiver). Derived categories (triangulated
categories, chain complexes, the homotopy category, localization of
categories, derived category of an algebra, Morita theory). Cohomolgy of
groups. Spectral sequences (filtrations, bicomplexes, Künneth’s Theorems). 
literature 
Rotman: An Introduction to Homological Algebra 
form of tuition 
Lecture 
mode of assessment 
written/oral
exam 