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Results tagged with ac.commutative-algebra
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user 5513
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
12
votes
Accepted
Free resolution dimension?
I'm sort of stealing the idea from t3suji, but here goes:
If the module is projective, i.e. $PD = 0$, then $FD \leq 1$.
If the module is not projective, i.e. $PD > 0$, then $PD = FD$.
The first sta …
- 4,790
11
votes
Accepted
Primes in a (commutative) Jacobson ring
The result is true in general.
We may assume a counterexample is given in the form of a domain $R$ satisfying the second property but with nontrivial Jacobson radical, i.e. the closed points of Spec …
- 4,790
4
votes
Orders of Number Fields
1) No. The normalization of a ring $R$ is never flat over $R$, unless $R$ was normal in the first place.
- 4,790
3
votes
Using schemes to prove things about rings
Primes in a (commutative) Jacobson ring
This question was phrased purely algebraically, but I only arrived at the solution by geometric arguments.