Theorems · Theorem · commutative algebra
completeIntegralClosure_eq_integralClosure
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsNoetherianRing R]
[IsDomain R] [IsFractionRing R S], completeIntegralClosure R S = integralClosure R S- Cited by
- 0 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- IsDomainstatement and proof · cited by 2,196
- Subalgebrastatement · cited by 1,353
- IsFractionRingstatement and proof · cited by 738
- IsNoetherianRingstatement and proof · cited by 268
- integralClosurestatement · cited by 105
- SetLike.extproof · cited by 92
- completeIntegralClosurestatement · cited by 4
- isAlmostIntegral_iff_isIntegralproof · cited by 1
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