If $A$ is a Dedekind domain and $a,b$ are ideals, then why does $aA_p⊂bA_p$ for every prime ideal $p$ imply that $a\subset b$?
I read it in Milne's notes but it alludes to DVR's and I'm not familiar with that concept.
If $A$ is a Dedekind domain and $a,b$ are ideals, then why does $aA_p⊂bA_p$ for every prime ideal $p$ imply that $a\subset b$?
I read it in Milne's notes but it alludes to DVR's and I'm not familiar with that concept.