Congruence Relations in Rings

Related lectures (32)

Page 3 of 4

Explores the construction of quotient rings and the properties of well-defined operations within rings.

Covers division rings, fields, and ideals in commutative rings with examples in Z and quaternions.

Explores discrete valuation rings, their properties, uniqueness of representation, and relationship with principal ideal domains.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Explores rings, domains, fields, and ideals, with a focus on constructions and properties.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

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

Covers primary decomposition in commutative rings and its application in prime ideals.

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

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