Commutative Rings and Fields

Related lectures (31)

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Covers the definition and properties of a field of fractions.

Explores fractional elements, equivalence relations, and injective mappings in commutative rings.

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

Covers commutative ring morphisms, subrings, and injective ring morphisms.

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

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

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

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

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

Explores canonical embedding of #-fields, lattices, and finiteness of class groups.