 Prime-ideal valuation in a Dedekind domain

ID: prime-ideal-valuation-in-a-dedekind-domain

For a nonzero ideal

I

v_{P} (I)

is the exponent of the nonzero prime ideal

P

I \subseteq J

if and only if

v_{P} (I) \geq v_{P} (J)

for every

P

, and

v_{P} (I + J) = min (v_{P} (I), v_{P} (J))

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