Concept

Principal ideal theorem

Related lectures (13)

Explores the discriminant in matrices, ideal class groups, and optimal embeddings in mathematics.

Covers the classical Lie algebras, focusing on calculations and dimensions.

Explores Hermite-Minkowski theorems in number fields and ideal classes.

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Covers the embeddings of number fields and ideal classes with proofs and examples.

Explores the properties and applications of logarithmic embeddings in number fields.

Covers the relations between the ideal class group and proper fractional ideals.

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

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

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

Explores the Chinese Remainder Theorem for Euclidean domains and the properties of commutative rings and fields.

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

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