Lectures related to Order (ring theory)

Covers the basics of solving polynomial equations, historical methods, matrix properties, imaginary numbers, and subrings in matrix algebras.

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

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

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

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

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