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Lecture
Geometric Primary Decomposition
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Related lectures (30)
Primary Decomposition in Commutative Rings
Covers primary decomposition in commutative rings and its application in prime ideals.
Primary Decomposition: Noetherian Ideal
Covers primary decomposition in Noetherian ideals and unique primary ideals.
Irreducible Algebraic Sets
Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.
Algebraic Subsets of A^1
Covers algebraic subsets of A^1 and ideals with a finite set of points.
Affine Algebraic Sets
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Sets and Operations: Introduction to Mathematics
Covers the basics of sets and operations in mathematics, from set properties to advanced operations.
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.
Mapping Functions and Surjections
Explores mapping functions, surjections, injective and surjective functions, and bijective functions.
Hilberts Nullstellensatz and Ideals
Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.
Algebraic Geometry: Localization and Prime Ideals
Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.
Cartesian Product and Induction
Introduces Cartesian product and induction for proofs using integers and sets.
Affine Varieties and Hypersurfaces
Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.
Local Rings and Residues
Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.
Functions: Definitions and Notations
Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.
Primary Decomposition in Rings
Explores primary decomposition in rings, focusing on primary ideals and their properties.
Ring Operations: Ideals and Classes
Covers the operations in rings, ideals, classes, and quotient rings.
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.
Dedekind Rings: Integral Extensions and Noetherian Rings
Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.
Linear Algebra: Sets and Operations
Introduces fundamental concepts of linear algebra, focusing on sets and operations.
Primary and Secondary Ideals
Covers the concept of primary and secondary ideals, focusing on uniqueness and invariance properties.
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