Regularity and Noetherian Local Rings

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Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

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

Explains the independence of events and sets in an algebraic context.

Introduces Lie algebras, vector spaces with a special bracket operation.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

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

Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.

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

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.