Lecture
Regularity and Integrality
Related lectures (77)
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Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
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Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.
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Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.
Rings and Fields
Explores rings, fields, ideals, and their properties 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.
Algebraic Geometry: Localization and Prime Ideals
Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.
Dedekind Rings: Theory and Applications
Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.
Local Rings and Minimal Primes
Explores local rings, Noetherian rings, and minimal primes in the context of integral domains.
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Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.
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