Timeline for going down theorem
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 20, 2015 at 15:49 | comment | added | Neil Epstein | Then no. Let $A$ be a Dedekind domain with non-torsion class group. Let $P$ be a prime of infinite order in said group. Let $B = \bigcap_{Q \in \text{Max} A, Q \neq P} A_Q$. Then I think $B$ is of finite type over $A$ (or anyway, I know some examples where it is), but it isn't faithfully flat (since $PB=B$), nor integral (since $A$ is integrally closed and has the same fraction field as $B$). And there's essentially nothing between $A$ and $B$ to make a factorization out of. But $B$ is going down over $A$. | |
| Mar 20, 2015 at 15:31 | comment | added | prochet | for example faithfully flat followed by integral. | |
| Mar 20, 2015 at 15:28 | comment | added | Neil Epstein | What sort of factorization do you want? | |
| Mar 16, 2015 at 14:50 | history | asked | prochet | CC BY-SA 3.0 |