Theorems · Theorem · commutative algebra
TensorProduct.toIntegralClosure_bijective_of_isLocalization
∀ {R : Type u_1} {S : Type u_2} {B : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : CommRing B] [inst_4 : Algebra R B] (M : Submonoid R) [IsLocalization M S],
Function.Bijective ⇑(TensorProduct.toIntegralClosure R S B)Localization preserves integral closure.
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- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
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- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
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- Ringproof · cited by 7,463
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerproof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- Submonoidstatement and proof · cited by 3,086
- TensorProductstatement and proof · cited by 2,545
- Subalgebrastatement · cited by 1,353
- RingHom.compproof · cited by 899
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