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Lecture
Discrete Valuation Rings
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Related lectures (32)
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Local Noetherian Rings
Covers local Noetherian rings, integrally closed domains, discrete valuations, and fraction fields.
Properties of Euclidean Domains
Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.
Finite Fields: Construction and Properties
Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.
Rings and Fields: Principal Ideals and Ring Homomorphisms
Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.
Algebra: Fundamental Theorem
Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.
Factorisation in Principal Ideal Domains
Explores factorisation in Principal Ideal Domains and the properties of prime numbers.
Dimension theory of rings
Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.
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.
Primary Decomposition: Noetherian Ideal
Covers primary decomposition in Noetherian ideals and unique primary ideals.
