Affine Algebraic Sets

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Related lectures (32)

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Properties of Finite Dimensional Algebras

Covers the properties of finite dimensional algebras and non-semisimple representations.

Dedekind Rings: Theory and Applications

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

Primary Decomposition in Commutative Rings

Covers primary decomposition in commutative rings and its application in prime ideals.

Morphisms between Affine Varieties

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.

Ring Operations: Ideals and Classes

Covers the operations in rings, ideals, classes, and quotient rings.

Algebraic Varieties in Linear Algebra

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

Dimension of Algebraic Variety

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

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.

Algebraic Structures: Modules and Morphisms

Explores modules, sub-modules, and morphisms in algebraic structures.

Algebraic Curves: Normalization

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