Rings and Fields: Principal Ideals and Ring Homomorphisms

This lecture covers the concepts of principal ideals, principal ideal domains, ring homomorphisms, subrings, characteristic of a ring, direct product of rings, commutative rings, zero divisors, integral domains, fields, ideals in a commutative ring, quotient rings, Chinese Remainder Theorem for integers, polynomial rings, Euclidean domains, maximal ideals in polynomial rings, irreducible polynomials, finite fields, and the construction and classification of finite fields.