Regularity and Noetherian Local Rings

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.