Ring Theory: Sub-rings and Morphisms

Related lectures (32)

Page 3 of 4

Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.

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

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

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

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

Explores Fermat's Theorem, factorization of integers, properties of Z[i], and Hurwitz quaternions.

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

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

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

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.