Ring Theory: Definitions and Examples

Related lectures (32)

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Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

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

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Covers the ring of polynomials, focusing on coefficients and multiplication.

Explores modules over a ring, injective morphisms, isomorphisms, and canonical groups.

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

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

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Introduces sub-rings and morphisms in ring theory, emphasizing stability by multiplication.