Theorems · Theorem · commutative algebra
IsIntegrallyClosed.integralClosure_eq_bot_iff
∀ {R : Type u_1} [inst : CommRing R] (K : Type u_3) [inst_1 : CommRing K] [inst_2 : Algebra R K]
[ifr : IsFractionRing R K], integralClosure R K = ⊥ ↔ IsIntegrallyClosed R- Cited by
- 3 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Bot.botstatement · cited by 4,720
- Subalgebrastatement · cited by 1,353
- IsFractionRingstatement and proof · cited by 738
- IsIntegrallyClosedstatement · cited by 203
- integralClosurestatement · cited by 105
- IsFractionRing.injectiveproof · cited by 70
- isIntegrallyClosed_iff_isIntegrallyClosedInproof · cited by 3
- IsIntegrallyClosedIn.integralClosure_eq_bot_iffproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsIntegrallyClosed.integralClosure_eq_botproof · cited by 2
- integralClosure.isIntegrallyClosedOfFiniteExtensionproof · cited by 0
- Valuation.Integers.isIntegrallyClosedproof · cited by 0