Lecture
Commutative Algebra: Recollections
Related lectures (46)
Rings and Fields: Principal Ideals and Ring Homomorphisms
Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.
Chinese Remainder Theorem: Rings and Fields
Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.
Dedekind Rings: Theory and Applications
Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.
Integral Domains: Factorisation and Noetherian Rings
Explores factorisation in Principal Ideal Domains and Noetherian rings, emphasizing the integral closure concept and the factorisation of ideals in Dedekind rings.
Rings and Fields
Explores rings, fields, ideals, and their properties in algebraic structures.
Finite Fields: Construction and Properties
Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.
Irreducible Factors and Noetherian Rings
Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.
Dimension Theory of Rings
Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
Congruence Relations in Rings
Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.
Affine Algebraic Sets
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.