The Stacks project

Exercise 111.64.2 (Theorems). Precisely but briefly state a nontrivial fact discussed in the lectures related to each item (if there is more than one then just pick one of them).

  1. Artinian rings,

  2. flatness and prime ideals,

  3. lengths of $A/\mathfrak m^ n$ for $(A, \mathfrak m)$ Noetherian local,

  4. the dimension formula for universally catenary Noetherian rings,

  5. completion of a Noetherian local ring, and

  6. Matlis duality for Artinian local rings.

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View Exercise 111.64.2 as pdf