Ring theory

Related lectures (32)

Page 3 of 4

Introduces ring theory, covering definitions, examples, and subrings criteria.

Covers the proof of Lagrange Theorem and explores quaternions, prime numbers, and equations.

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Explores Diffie-Hellman key exchange, ElGamal cryptosystem, and their security applications in cryptography.

Covers non-degenerate integral quadratic lattices and adèles, including their properties and definitions.

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

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

Introduces affine varieties and covers morphisms between them and their coordinate rings.