Write a few:
- as ever in discussing PIDs, bear in mind Z and K[x]
- statement & interpretation of result
  + equivalence via Chinese Remainder Theorem
  + naturalness & lack thereof
  + comment on the free part being a bit weird
(prime ideals of different heights/lengths??)
  algebraic geometry POV: slice horizontally vs. vertically
  (module is a (coherent) sheaf over affine scheme;
   over point, it's not 2 points, but a 2D vector space)

- free resolution proof: presentation, Smith Normal Form
  --> homological algebra

- intrinsic proof via filtration
  --> Wederburn-Artin

- primary resolution is a Hasse principle:
  if know module at every prime
  (and modules over a DVR are very easy;
   next simpler than vector space)
  ...then know whole module

- subtle homological interpretation:
  torsion is weird! (Tor = Tor^1 !!)
  tensoring is easier (from this POV)
