Localization Theorem in Dedekind Rings

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Ideals and Representations

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

Chinese Remainder Theorem: Rings and Fields

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

Ideals and PPCM

Covers the concept of ideals in polynomial rings and their properties.

Idempotent Elements and Central Orthogonal

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Integral Domains: Factorisation and Noetherian Rings

Explores factorisation in Principal Ideal Domains and Noetherian rings, emphasizing the integral closure concept and the factorisation of ideals in Dedekind rings.

Hilberts Nullstellensatz and Ideals

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

Division Rings and Ideals

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

Ramification Theory: Residual Fields and Discriminant Ideal

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

Rings and Fields

Explores rings, fields, ideals, and their properties in algebraic structures.

Finite Fields: Construction and Properties

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.