Integrity in Algebra

Related lectures (32)

Page 2 of 4

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

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

Explores rings, domains, fields, and ideals, with a focus on constructions and properties.

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Explores operations on ideals and structure theorems in commutative rings.

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

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

Discusses Fermat's equation and Gaussian integers' properties.