Can anyone explain me why the integral closure of a PID $A$ in a separable finite extension of its fraction field is a torsion-free $A$-module?
I know that it is a finitely generated $A$-module, but how can i prove that? Thanks in advance...
2026-03-28 06:24:00.1774679040
Integral closure of a PID is torsion-free
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Pick $b\in B$ and $a\in A$ such that $ab=0$ and see this in $L$. What do you get?