Theorems · Theorem · commutative algebra
IsIntegrallyClosed.iInf
∀ {R : Type u_1} {K : Type u_2} [inst : CommRing R] [inst_1 : Field K] [inst_2 : Algebra R K] [IsFractionRing R K]
{ι : Type u_3} (S : ι → Subalgebra R K), (∀ (i : ι), IsIntegrallyClosed ↥(S i)) → IsIntegrallyClosed ↥(⨅ i, S i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerproof · cited by 3,896
- iInfstatement and proof · cited by 1,690
- Subalgebrastatement and proof · cited by 1,353
- IsFractionRingstatement and proof · cited by 738
- AlgHom.toRingHomproof · cited by 490
- IsIntegralproof · cited by 427
- RingHom.toAlgebraproof · cited by 337
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