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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.
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
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
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.
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