Lectures related to Completion of a Field: Algebraic Closure

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

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

Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

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

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Covers the concept of ideals in polynomial rings and their properties.

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

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

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