Affine Algebraic Varieties: Zariski Topology

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Affine Varieties Log in to Mediaspace to watch this video

Introduces affine varieties and covers morphisms between them and their coordinate rings.

Affine Varieties and Hypersurfaces Log in to Mediaspace to watch this video

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Dimension of Algebraic Variety Log in to Mediaspace to watch this video

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

Affine Algebraic Sets Log in to Mediaspace to watch this video

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Dimension Theory of Rings Log in to Mediaspace to watch this video

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Algebraic Geometry: Localization and Prime Ideals Log in to Mediaspace to watch this video

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Algebraic Varieties: Projective Sets and Topology Log in to Mediaspace to watch this video

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

Primary Decomposition in Commutative Rings Log in to Mediaspace to watch this video

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

Idempotent Elements and Central Orthogonal Log in to Mediaspace to watch this video

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Algebraic Subsets of A^1 Log in to Mediaspace to watch this video

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

Modern Algebraic Geometry Log in to Mediaspace to watch this video

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Dedekind Rings: Integral Extensions and Noetherian Rings Log in to Mediaspace to watch this video

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

Ring Operations: Ideals and Classes Log in to Mediaspace to watch this video

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

Irreducible Algebraic Sets Log in to Mediaspace to watch this video

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

Regular Implicit Functions Log in to Mediaspace to watch this video

Discusses regular implicit functions, rings, ideals, sheaves, and ring operations.

Galois Theory: Dedekind Rings Log in to Mediaspace to watch this video

Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Additivity of Dimension & Height Log in to Mediaspace to watch this video

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

Symbolic Powers: Interpretation and Applications Log in to Mediaspace to watch this video

Covers the interpretation and applications of symbolic powers in algebraic structures, focusing on Krull's Hauptideal Satz and Noetherian rings.

Factorisation in Dedekind Ring Log in to Mediaspace to watch this video

Explains the factorisation of ideals in a Dedekind ring using prime ideals and covers ramification index, residual fields, inertia degree, and properties of Dedekind rings.

Factorisation in Principal Ideal Domains Log in to Mediaspace to watch this video

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.

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