[_hardwaregeek]

Interesting seeing this defined from a functional programming/category theory perspective. Personally I like examples for my algebraic structures along with some simple proofs why they're that structure. What was extremely useful for my Algebra class was a Wikipedia note detailing the hierarchy of rings via set inclusion:

    commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ finite fields

Found here: https://en.wikipedia.org/wiki/Integral_domain