Lectures related to Irreducible Algebraic Sets

Mathematical structures: selected topics

Covers selected mathematical topics including numbers, approximations, algebraic structures, limits, and series.

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

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.

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.

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.

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.

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.

Geometric Primary Decomposition Log in to Mediaspace to watch this video

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

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.

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.

Affine Algebraic Varieties: Zariski Topology Log in to Mediaspace to watch this video

Explores affine algebraic varieties, emphasizing the Zariski Topology and regular functions.

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.

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.

Projective Space and Algebraic Sets Log in to Mediaspace to watch this video

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

Primary Decomposition: Understanding Schemes Log in to Mediaspace to watch this video

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.

Prime ideals and local rings Log in to Mediaspace to watch this video

Covers the concept of prime ideals and local rings, emphasizing their importance.

Separable Extensions: Dedekind Rings Log in to Mediaspace to watch this video

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.

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.

Dedekind Function: Analytic Continuation and Euler Product Formula Log in to Mediaspace to watch this video

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

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.