Local Rings and Residues

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Related lectures (31)

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Ideals and Representations

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

Hilberts Nullstellensatz and Ideals

Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.

Principal Ideal Domains: Structure and Homomorphisms

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

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Local structure of totally disconnected locally compact groups III

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Chinese Remainder Theorem: Rings and Fields

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

Dedekind Rings and Fractional Ideals

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.