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bump to nightly-2023-07-04-09
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leanprover-community-bot committed Jul 4, 2023
1 parent 0989637 commit 8a4e8ca
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2 changes: 1 addition & 1 deletion Mathbin/AlgebraicGeometry/PrimeSpectrum/Basic.lean
Expand Up @@ -800,7 +800,7 @@ theorem comap_singleton_isClosed_of_isIntegral (f : R →+* S) (hf : f.IsIntegra
(x : PrimeSpectrum S) (hx : IsClosed ({x} : Set (PrimeSpectrum S))) :
IsClosed ({comap f x} : Set (PrimeSpectrum R)) :=
(isClosed_singleton_iff_isMaximal _).2
(Ideal.isMaximal_comap_of_isIntegral_of_is_maximal' f hf x.asIdeal <|
(Ideal.isMaximal_comap_of_isIntegral_of_isMaximal' f hf x.asIdeal <|
(isClosed_singleton_iff_isMaximal x).1 hx)
#align prime_spectrum.comap_singleton_is_closed_of_is_integral PrimeSpectrum.comap_singleton_isClosed_of_isIntegral
-/
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6 changes: 3 additions & 3 deletions Mathbin/RingTheory/Ideal/Over.lean
Expand Up @@ -353,11 +353,11 @@ theorem isMaximal_comap_of_isIntegral_of_isMaximal (hRS : Algebra.IsIntegral R S
#align ideal.is_maximal_comap_of_is_integral_of_is_maximal Ideal.isMaximal_comap_of_isIntegral_of_isMaximal
-/

#print Ideal.isMaximal_comap_of_isIntegral_of_is_maximal' /-
theorem isMaximal_comap_of_isIntegral_of_is_maximal' {R S : Type _} [CommRing R] [CommRing S]
#print Ideal.isMaximal_comap_of_isIntegral_of_isMaximal' /-
theorem isMaximal_comap_of_isIntegral_of_isMaximal' {R S : Type _} [CommRing R] [CommRing S]
(f : R →+* S) (hf : f.IsIntegral) (I : Ideal S) (hI : I.IsMaximal) : IsMaximal (I.comap f) :=
@isMaximal_comap_of_isIntegral_of_isMaximal R _ S _ f.toAlgebra hf I hI
#align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_is_maximal'
#align ideal.is_maximal_comap_of_is_integral_of_is_maximal' Ideal.isMaximal_comap_of_isIntegral_of_isMaximal'
-/

section IsIntegralClosure
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14 changes: 7 additions & 7 deletions Mathbin/RingTheory/IntegralClosure.lean
Expand Up @@ -701,21 +701,21 @@ theorem integralClosure.isIntegral (x : integralClosure R A) : IsIntegral R x :=
#align integral_closure.is_integral integralClosure.isIntegral
-/

#print RingHom.is_integral_of_is_integral_mul_unit /-
theorem RingHom.is_integral_of_is_integral_mul_unit (x y : S) (r : R) (hr : f r * y = 1)
#print RingHom.isIntegral_of_isIntegral_mul_unit /-
theorem RingHom.isIntegral_of_isIntegral_mul_unit (x y : S) (r : R) (hr : f r * y = 1)
(hx : f.IsIntegralElem (x * y)) : f.IsIntegralElem x :=
by
obtain ⟨p, ⟨p_monic, hp⟩⟩ := hx
refine' ⟨scale_roots p r, ⟨(monic_scale_roots_iff r).2 p_monic, _⟩⟩
convert scale_roots_eval₂_eq_zero f hp
rw [mul_comm x y, ← mul_assoc, hr, one_mul]
#align ring_hom.is_integral_of_is_integral_mul_unit RingHom.is_integral_of_is_integral_mul_unit
#align ring_hom.is_integral_of_is_integral_mul_unit RingHom.isIntegral_of_isIntegral_mul_unit
-/

#print isIntegral_of_isIntegral_mul_unit /-
theorem isIntegral_of_isIntegral_mul_unit {x y : A} {r : R} (hr : algebraMap R A r * y = 1)
(hx : IsIntegral R (x * y)) : IsIntegral R x :=
(algebraMap R A).is_integral_of_is_integral_mul_unit x y r hr hx
(algebraMap R A).isIntegral_of_isIntegral_mul_unit x y r hr hx
#align is_integral_of_is_integral_mul_unit isIntegral_of_isIntegral_mul_unit
-/

Expand All @@ -728,11 +728,11 @@ theorem isIntegral_of_mem_closure' (G : Set A) (hG : ∀ x ∈ G, IsIntegral R x
#align is_integral_of_mem_closure' isIntegral_of_mem_closure'
-/

#print is_integral_of_mem_closure'' /-
theorem is_integral_of_mem_closure'' {S : Type _} [CommRing S] {f : R →+* S} (G : Set S)
#print isIntegral_of_mem_closure'' /-
theorem isIntegral_of_mem_closure'' {S : Type _} [CommRing S] {f : R →+* S} (G : Set S)
(hG : ∀ x ∈ G, f.IsIntegralElem x) : ∀ x ∈ Subring.closure G, f.IsIntegralElem x := fun x hx =>
@isIntegral_of_mem_closure' R S _ _ f.toAlgebra G hG x hx
#align is_integral_of_mem_closure'' is_integral_of_mem_closure''
#align is_integral_of_mem_closure'' isIntegral_of_mem_closure''
-/

#print IsIntegral.pow /-
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