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Lecture
Irreducible Factors and Noetherian Rings
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Related lectures (32)
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Properties of Euclidean Domains
Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.
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.
Factorisation in PIDs
Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.
Finite Fields: Construction and Properties
Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.
Simple Modules: Schur's Lemma
Covers simple modules, endomorphisms, and Schur's lemma in module theory.
Dedekind Rings: Integral Extensions and Noetherian Rings
Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.
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.
Idempotent Elements and Central Orthogonal
Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.
Primary Decomposition: Noetherian Ideal
Covers primary decomposition in Noetherian ideals and unique primary ideals.
