feat: port RingTheory.Multiplicity (#2962)

Co-authored-by: Rémy Degenne <remydegenne@gmail.com>

Author: mattrobball

Mathlib.lean

@@ -1271,6 +1271,7 @@ import Mathlib.RingTheory.Ideal.Prod
 import Mathlib.RingTheory.Ideal.Quotient
 import Mathlib.RingTheory.Localization.Basic
 import Mathlib.RingTheory.Localization.Integer
+import Mathlib.RingTheory.Multiplicity
 import Mathlib.RingTheory.MvPolynomial.Tower
 import Mathlib.RingTheory.Nilpotent
 import Mathlib.RingTheory.NonZeroDivisors