[Merged by Bors] - feat: Generalize absNorm to fractional ideals #9613
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This PR defines the absolute ideal norm of a fractional ideal `I : FractionalIdeal R⁰ K` where `K` is a fraction field of `R` as a zero-preserving group homomorphism with values in `ℚ` and proves that it generalises the norm on (integral) ideals (and some other classical result). Also in this PR: - Add the directory `Mathlib/RingTheory/FractionalIdeal` and move the file `Mathlib/RingTheory/FractionalIdeal.lean` to `Mathlib/RingTheory/FractionalIdeal/Basic.lean`. The new results are in `Mathlib/RingTheory/FractionalIdeal/Norm.lean` - Define the `numerator` and `denominator` of a fractional ideal. These are used to define the norm. Also define a linear equiv between a fractional ideal and its `numerator`. - Several technical lemmas.
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This PR defines the absolute ideal norm of a fractional ideal
I : FractionalIdeal R⁰ KwhereKis a fraction field ofRas a zero-preserving group homomorphism with values inℚand proves that it generalises the norm on (integral) ideals (and some other classical result).Also in this PR:
Mathlib/RingTheory/FractionalIdealand move the fileMathlib/RingTheory/FractionalIdeal.leantoMathlib/RingTheory/FractionalIdeal/Basic.lean. The new results are inMathlib/RingTheory/FractionalIdeal/Norm.leannumeratoranddenominatorof a fractional ideal. These are used to define the norm. Also define a linear equiv between a fractional ideal and itsnumerator.