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Merge branch 'master' into IsGalois
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mbkybky committed Oct 29, 2024
2 parents d3ee291 + c78385b commit 9103f7c
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28 changes: 0 additions & 28 deletions GaloisRamification/GaloisRamification.lean
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Expand Up @@ -89,34 +89,6 @@ theorem prime_iff_isMaximal {p : Ideal A} (hp0 : p ≠ ⊥) : Prime p ↔ p.IsMa
fun hp ↦ (isPrime_of_prime hp).isMaximal hp.ne_zero,
fun hp ↦ prime_of_isPrime hp0 hp.isPrime⟩

namespace Ideal
-- lemmas of isomorphisms act on ideals
/-- A ring isomorphism sends a prime ideal to a prime ideal. -/
instance {R S E : Type*} [CommRing R] [CommRing S] (p : Ideal R) [p.IsPrime] [EquivLike E R S]
[RingEquivClass E R S] (e : E) : (map e p).IsPrime := by
exact map_isPrime_of_equiv e

/-- A ring isomorphism sends a maximal ideal to a maximal ideal. -/
instance map_isMaximal_of_equiv {R S E : Type*} [Ring R] [Ring S] (p : Ideal R)
[hp : p.IsMaximal] [EquivLike E R S] [RingEquivClass E R S] (e : E) : (map e p).IsMaximal :=
map.isMaximal e (EquivLike.bijective e) hp

/-- A maximal ideal pull back by a ring isomorphism is a maximal ideal. -/
instance comap_isMaximal_of_equiv {R S E : Type*} [Ring R] [Ring S] (p : Ideal S)
[p.IsMaximal] [EquivLike E R S] [RingEquivClass E R S] (e : E) : (comap e p).IsMaximal :=
comap_isMaximal_of_surjective e (EquivLike.surjective e)

theorem mem_map_of_equiv {R S E : Type*} [Semiring R] [Semiring S] (I : Ideal R)
[EquivLike E R S] [RingEquivClass E R S] (e : E) (y : S) : y ∈ map e I ↔ ∃ x ∈ I, e x = y := by
constructor
· intro h
simp_rw [show map e I = _ from map_comap_of_equiv I (e : R ≃+* S)] at h
exact ⟨(e : R ≃+* S).symm y, h, RingEquiv.apply_symm_apply (e : R ≃+* S) y⟩
· rintro ⟨x, hx, rfl⟩
exact mem_map_of_mem e hx

end Ideal

end lie_over

section transitive
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1 change: 1 addition & 0 deletions GaloisRamification/ToMathlib.lean
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Expand Up @@ -9,6 +9,7 @@ import Mathlib.RingTheory.Valuation.ValuationRing

import GaloisRamification.ToMathlib.Finite
import GaloisRamification.ToMathlib.FractionRing
import GaloisRamification.ToMathlib.IsGalois
import GaloisRamification.ToMathlib.Normal
import GaloisRamification.ToMathlib.restrictScalarsHom
import GaloisRamification.ToMathlib.separableClosure
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4 changes: 2 additions & 2 deletions lake-manifest.json
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Expand Up @@ -5,7 +5,7 @@
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