Mathematical structures: selected topics

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Related lectures (36)

Fractions of Rings Log in to Mediaspace to watch this video

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

Regular Implicit Functions Log in to Mediaspace to watch this video

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

Galois Theory: Dedekind Rings Log in to Mediaspace to watch this video

Explores Galois theory with a focus on Dedekind rings and their unique factorization of fractional ideals.

Algebraic Structures: Fields and Vectorial Spaces Log in to Mediaspace to watch this video

Covers prime numbers, vectors, 3D geometry, crystallography, and algebraic structures in materials science.

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.

Factorisation in PIDs Log in to Mediaspace to watch this video

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

Chinese Remainder Theorem Log in to Mediaspace to watch this video

Explores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.

Symbolic Powers: Interpretation and Applications Log in to Mediaspace to watch this video

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

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.

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.

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.

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.

Continuity: Limits, Sequences, and Algebraic Operations Log in to Mediaspace to watch this video

Explores limits, sequences, algebraic operations, and continuity in real numbers.

Lie Algebras: Introduction and Structure Log in to Mediaspace to watch this video

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

Sequences and Convergence: Understanding Mathematical Foundations Log in to Mediaspace to watch this video

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Structure of Algebras Log in to Mediaspace to watch this video

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

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