General
Main content blocks
- Lecturer: Profile: Dawid Kielak
Course information
General Prerequisites:
Rings and Modules is essential. Galois Theory is strongly recommended.
Course Term: Hilary
Course Lecture Information: 16 lectures
Course Weight: 1
Course Level: H
Assessment Type: Written Examination
Course Overview:
Amongst the most familiar objects in mathematics are the ring of integers and the polynomial rings over fields. These play a fundamental role in number theory and in algebraic geometry, respectively. The course explores the basic properties of such rings.
Course Synopsis:
Modules, ideals, prime ideals, maximal ideals.
Noetherian rings; Hilbert basis theorem. Minimal primes.
Localization.
Polynomial rings and algebraic sets. Weak Nullstellensatz.
Nilradical and Jacobson radical; strong Nullstellensatz.
Integral extensions. Prime ideals in integral extensions.
Noether Normalization Lemma.
Krull dimension; dimension of an affine algebra.
Noetherian rings of small dimension, Dedekind domains.
Noetherian rings; Hilbert basis theorem. Minimal primes.
Localization.
Polynomial rings and algebraic sets. Weak Nullstellensatz.
Nilradical and Jacobson radical; strong Nullstellensatz.
Integral extensions. Prime ideals in integral extensions.
Noether Normalization Lemma.
Krull dimension; dimension of an affine algebra.
Noetherian rings of small dimension, Dedekind domains.
Section outline
-
-
Opened: Saturday, 11 January 2025, 12:00 AMDue: Monday, 3 February 2025, 9:00 AM
-
Opened: Monday, 3 February 2025, 5:37 PMDue: Monday, 17 February 2025, 9:00 AM