Congruence Relations in Rings

This lecture covers congruence relations in a ring, the relationship between ideals and congruence relations in a commutative ring, the ring structure on the set of congruence classes, principal ideals, principal ideal domains (PID), ring homomorphisms, the kernel of a ring homomorphism, the image as a subring, homomorphisms between Z/nZ and Z/mZ, the characteristic of a ring, and the characteristic of a direct product of rings.