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Lecture
Primary Decomposition: Noetherian Ideal
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Primary Decomposition in Rings
Explores primary decomposition in rings, focusing on primary ideals and their properties.
Primary Decomposition: Understanding Schemes
Explores primary decomposition and schemes in algebraic geometry, emphasizing the importance of working over non-algebraically closed fields and the concept of fibers of morphisms.
Primary Decomposition in Commutative Rings
Covers primary decomposition in commutative rings and its application in prime ideals.
Irreducible Factors and Noetherian Rings
Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.
Dedekind Rings: Theory and Applications
Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.
Commutative Algebra: Recollections
Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.
Geometric Primary Decomposition
Covers radical ideals, Nullstellensatz, primary ideals, and algebraic sets.
Symbolic Powers: Interpretation and Applications
Covers the interpretation and applications of symbolic powers in algebraic structures, focusing on Krull's Hauptideal Satz and Noetherian rings.
Irreducible Factors and Noetherian Rings
Discusses irreducible factors in rings and the properties of Noetherian rings.
Ring Operations: Ideals and Classes
Covers the operations in rings, ideals, classes, and quotient rings.
