Commutative algebra

Course Code :1001WETCOA
Study domain:Mathematics
Academic year:2017-2018
Semester:1st semester
Contact hours:60
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:English
Exam period:exam in the 1st semester
Lecturer(s)Kevin De Laet

3. Course contents *

  • Commutative rings, ideals, maximal ideals, prime ideals, radical ideals, local rings, Nakayama's Lemma.
  • Modules.
  • Integral extensions: integral closure, going-up, going-down theorems for chains of prime ideals, Noether Normalization.
  • Dimension theory: definition of Krull dimension in relation to the transcendence degree for algebras over a field.
  • Noetherian rings: Hilbert's basis theorem, regular local rings.
  • Affine algebras: Zariski's Lemma, Hilbert's Nullstellensatz.
  • Artinian rings and modules, modules of finite length.
  • Dedekind rings and characterization of discrete valuation rings.
  • Number fields, applications to problems from algebraic number theory.