Lectures related to Cyclotomic Extensions: Norms, Ideals, and Primes

Mathematical structures: selected topics

Covers selected mathematical topics including numbers, approximations, algebraic structures, limits, and series.

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

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Prime Numbers and Primality Testing

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Polynomials, Division, and Ideals

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

Frobenius Theorems in Number Theory Log in to Mediaspace to watch this video

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Dimension Theory of Rings Log in to Mediaspace to watch this video

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

Ring Operations: Ideals and Classes Log in to Mediaspace to watch this video

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

Localization and Ideals Log in to Mediaspace to watch this video

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

Dedekind Rings: Factorisation and Ideal Class Group Log in to Mediaspace to watch this video

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

Dedekind Rings and Fractional Ideals Log in to Mediaspace to watch this video

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

Prime ideals and local rings Log in to Mediaspace to watch this video

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

Primary Decomposition in Commutative Rings Log in to Mediaspace to watch this video

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

Idempotent Elements and Central Orthogonal Log in to Mediaspace to watch this video

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

Factorisation in PIDs Log in to Mediaspace to watch this video

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.

Regular Implicit Functions Log in to Mediaspace to watch this video

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

Ideals and Representations Log in to Mediaspace to watch this video

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

Primary and Secondary Ideals Log in to Mediaspace to watch this video

Covers the concept of primary and secondary ideals, focusing on uniqueness and invariance properties.

Hilberts Nullstellensatz and Ideals Log in to Mediaspace to watch this video

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

Irreducible Factors and Noetherian Rings Log in to Mediaspace to watch this video

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.