Kernels of ring homomorphisms, quotients, ideals as representing kernels

[plt-amy]

Essentially the same thing as Algebra.Group.Subgroup, but for ring/ideal rather than group/normal subgroup. Snarky wording about subsets and evil wizards is mandatory.

• Images of ring homomorphisms
• Kernels of ring homomorphisms
• "im(f)" satisfies the universal property of "R/ker(f)"
• Ideal
• Quotient by an ideal
• Kernel of the quotient map is the ideal we started with