Lecture

Completion of a Field: Algebraic Closure

Related lectures (32)

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.

Covers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.

Covers the operations and properties of rings, focusing on ideals and quotients.

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Explores rings, fields, ideals, and their properties in algebraic structures.

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

Explores the calculation of generators of ideals and their significance in mathematical operations.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Explores operations on ideals and structure theorems in commutative rings.

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