Let $A$ be an artin ring with finitely many maximal ideals $\{{\mathfrak{m}}_1,\dots ,{\mathfrak{m}}_{\mathfrak{n}}\}$. Then the following hold:

1. $A$ is isomorphic to a direct sum of 1;;local artin rings.
2. The summands are unique up to isomorphism/rearranging
   PROOF:

• Part 1 is CRT and 9. Proposition 4.8.4
• Part 2 uses uniqueness of a minimal primary decomposition