Concept

Irreducible component

Related lectures (14)

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.

Tangent Spaces and Varieties

Explores the relationship between tangent spaces and dimension in algebraic geometry.

Algebraic Subsets of A^1

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Projective Varieties: An Algebraic Study

Covers the study of projective varieties and their relation to compact manifolds.

Algebraic Varieties in Linear Algebra

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.

Algebraic Varieties: Projective Sets and Topology

Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.

Remarks about the Quotient

Explores the concept of the quotient in linearly reductive groups and varieties, discussing irreducibility, normality, and integral properties.

Projective Space and Algebraic Sets

Introduces projective space and algebraic sets, discussing homogeneous coordinates, ideals, and generators.

Ring Constructions: Structure Theorems

Explores operations on ideals and structure theorems in commutative rings.

Geometric Primary Decomposition

Covers radical ideals, Nullstellensatz, primary ideals, and algebraic sets.

Polynomial Rings and Irreducibility Criteria

Covers polynomial rings, irreducibility criteria, and algebraic structures in fields.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Field of Rational Functions

Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.

Primary Decomposition: Noetherian Ideal

Covers primary decomposition in Noetherian ideals and unique primary ideals.