Integral Domains: Factorisation and Noetherian Rings

Related lectures (32)

Page 3 of 4

Explores local rings, Noetherian rings, and minimal primes in the context of integral domains.

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.

Discusses irreducible factors in rings and the properties of Noetherian rings.

Covers the properties of the ring of Eisenstein integers and its submodule structure.

Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Explores the Localization Theorem in Dedekind rings, isomorphism induced by injection, and ramification in field theory.

Covers the interpretation and applications of symbolic powers in algebraic structures, focusing on Krull's Hauptideal Satz and Noetherian rings.

Covers simple modules, endomorphisms, and Schur's lemma in module theory.