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feat: add coe instances for spectrums #37343

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feat: add coe instances for spectrums #37343

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3 changes: 3 additions & 0 deletions Mathlib/RingTheory/DedekindDomain/Ideal/Lemmas.lean
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Expand Up @@ -467,6 +467,9 @@ instance isMaximal : v.asIdeal.IsMaximal := v.isPrime.isMaximal v.ne_bot

theorem prime : Prime v.asIdeal := Ideal.prime_of_isPrime v.ne_bot v.isPrime

instance : Coe (HeightOneSpectrum R) (Ideal R) where
coe P := P.asIdeal

/--
The (nonzero) prime elements of the monoid with zero `Ideal R` correspond
to an element of type `HeightOneSpectrum R`.
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3 changes: 3 additions & 0 deletions Mathlib/RingTheory/Spectrum/Maximal/Defs.lean
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Expand Up @@ -29,3 +29,6 @@ structure MaximalSpectrum (R : Type*) [CommSemiring R] where
isMaximal : asIdeal.IsMaximal

attribute [instance] MaximalSpectrum.isMaximal

instance (R : Type*) [CommSemiring R] : Coe (MaximalSpectrum R) (Ideal R) where
coe P := P.asIdeal
3 changes: 3 additions & 0 deletions Mathlib/RingTheory/Spectrum/Prime/Defs.lean
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Expand Up @@ -49,6 +49,9 @@ See the corresponding section at `Mathlib/RingTheory/Spectrum/Prime/Topology.lea

variable {R : Type*} [CommSemiring R]

instance : Coe (PrimeSpectrum R) (Ideal R) where
coe P := P.asIdeal

instance : PartialOrder (PrimeSpectrum R) :=
PartialOrder.lift asIdeal (@PrimeSpectrum.ext _ _)

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