Finite Fields: Construction and Properties

This lecture covers the construction and properties of finite fields, including the quotient of a PID over a maximal ideal resulting in a field, irreducible polynomials, and the classification of finite fields. It also discusses rings and fields, commutative rings, zero divisors, integral domains, fields, principal ideal domains, polynomial rings, Euclidean domains, and the Chinese Remainder Theorem for integers and Euclidean domains.