discipline 
Pure Mathematics

subject 
Commutative
Algebra

lecturers 
József Pelikán, Gyula Károlyi 
credits 
2 
period 

curriculum 
Prime and primary ideals, nilradical,
Jacobson radical. Zariski topology, Krull dimension. Factor rings and factor modules. Local
properties, local rings. Primary decomposition of ideals, cases of unicity. Integral dependence, integrally closed rings.
The Going Up and Going Down theorems. Valuation rings. Noetherian
rings, the Lasker–Noether
theorem. Artinian rings, structure theorem.
Discrete valuation domains, Dedekind domains.
Dimension theory, Hilbert function. Regular local rings. Gröbner
bases. 
literature 
AtiyahMacDonald: Introduction to Commutative
Algebra 
form of tuition 
Lecture 
mode of assessment 
written/oral exam 