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 LaskerNoether theorem. Artinian rings, structure theorem. Discrete valuation domains, Dedekind domains. Dimension theory, Hilbert function. Regular local rings. Gröbner bases.

literature

Atiyah-MacDonald: Introduction to Commutative Algebra

form of tuition

Lecture

mode of assessment

written/oral exam