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fix
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mbkybky committed Oct 29, 2024
1 parent 9103f7c commit 6caa12b
Showing 1 changed file with 5 additions and 5 deletions.
10 changes: 5 additions & 5 deletions GaloisRamification/ToMathlib/restrictScalarsHom.lean
Original file line number Diff line number Diff line change
Expand Up @@ -36,7 +36,7 @@ theorem reverse_map_uniqueness {F S : Type*}
[Algebra F S]
(h : Module.finrank F S = 1)
(w: S) {y: F}
(h1: y • 1 = w): y = (reverse_map_if_rank_eq_one h).1 w := by
(h1: y • 1 = w) : y = (reverse_map_if_rank_eq_one h).1 w := by
have h2 := (reverse_map_if_rank_eq_one h).2 w
rw [<-h2] at h1
apply_fun (fun x => x • (1: S))
Expand Down Expand Up @@ -84,7 +84,7 @@ theorem reverse_hom_smul_one_eq_self {F S : Type*}
[Field F] [CommRing S] [Nontrivial S]
[Algebra F S]
(h : Module.finrank F S = 1)
(w: S): (reverse_hom_if_rank_eq_one h w) • 1 = w :=(reverse_map_if_rank_eq_one h).2 w
(w: S) : (reverse_hom_if_rank_eq_one h w) • 1 = w :=(reverse_map_if_rank_eq_one h).2 w

/-- the reverse homomorphism is an algebra homomorphism
-/
Expand Down Expand Up @@ -125,7 +125,7 @@ noncomputable def reverse_algebra_if_rank_eq_one {F S : Type*}
rw [add_smul]
repeat rw [reverse_hom_smul_one_eq_self]

noncomputable def reverse_algebra_is_scalar_tower {F S A : Type*}
noncomputable def reverse_algebra_is_scalar_tower {F S : Type*} (A : Type*)
[Semiring A]
[Field F] [CommRing S] [Nontrivial S]
[Algebra S A] [Algebra F A][Algebra F S]
Expand All @@ -148,15 +148,15 @@ noncomputable def reverse_algebra_is_scalar_tower {F S A : Type*}



noncomputable def aut_equiv_of_finrank_eq_one {F S A : Type*}
noncomputable def aut_equiv_of_finrank_eq_one {F S : Type*} (A : Type*)
[Semiring A]
[Field F] [CommRing S] [Nontrivial S]
[Algebra S A] [Algebra F A][Algebra F S]
[IsScalarTower F S A]
(h : Module.finrank F S = 1)
: (A ≃ₐ[S] A) ≃* (A ≃ₐ[F] A) where
toFun := AlgEquiv.restrictScalarsHom F S A
invFun := @AlgEquiv.restrictScalarsHom S F A _ _ _ (reverse_algebra_if_rank_eq_one h) _ _ (reverse_algebra_is_scalar_tower h)
invFun := @AlgEquiv.restrictScalarsHom S F A _ _ _ (reverse_algebra_if_rank_eq_one h) _ _ (reverse_algebra_is_scalar_tower A h)
left_inv := by
intro x
apply AlgEquiv.ext
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