Algebraic Geometry: Localization and Prime Ideals

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 1 of 4

Dimension Theory of Rings

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

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Separable Extensions: Dedekind Rings

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

Dedekind Rings: Integral Extensions and Noetherian Rings

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

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Primary Decomposition in Commutative Rings

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

Dedekind Rings and Fractional Ideals

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Affine Algebraic Sets

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

Idempotent Elements and Central Orthogonal

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

Additivity of Dimension & Height

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