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This problem has Hartshorne Height 1.
- a) This is a standard set of equivalences in commutative algebra.
- b) Choose a cover with no finite subcover, and construct an infinite descending chain of closed subsets (the complement of some ascending chain of open sets)
- c) For with Noetherian and irreducible, use topology to show so chains must stablize in
- d)Proceed by contradiction, (i.e. there are infinitely many point) pick two distinct points and separate them by disjoint opens. Use the complement of the opens to write where the closed. At least one must have infinitely points, and also Hausdorff and Noeth. Construct infinite descending chain...