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Localization and Ideals
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Related lectures (32)
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Ring Operations: Ideals and Classes
Covers the operations in rings, ideals, classes, and quotient rings.
Dimension Theory of Rings
Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
Chinese Remainder Theorem: Rings and Fields
Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.
Idempotent Elements and Central Orthogonal
Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.
Galois Theory: Dedekind Rings
Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.
Fractions of Rings
Explores the concept of fractions of rings and their uniqueness in ideals and quotients.
Principal Ideal Domains: Structure and Homomorphisms
Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.
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.
Dedekind Rings: Factorisation and Ideal Class Group
Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.
Polynomials, Division, and Ideals
Explores polynomials, their operations, and the concept of ideals in polynomial rings.
