The Stacks project

Exercise 111.64.1 (Definitions). Provide brief definitions of the italicized concepts.

  1. a multiplicative subset of a ring $A$,

  2. an Artinian ring $A$,

  3. the spectrum of a ring $A$ as a topological space,

  4. a flat ring map $A \to B$,

  5. the height of a prime ideal $\mathfrak p$ in $A$, and

  6. the functors $\text{Tor}^ A_ i(-, -)$ over a ring $A$.

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View Exercise 111.64.1 as pdf