Theorems · Theorem · commutative algebra
isAlmostIntegral_iff_isIntegral
∀ {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] {s : S}, IsAlmostIntegral R s ↔ IsIntegral R s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- IsFractionRingstatement and proof · cited by 738
- IsIntegralstatement · cited by 427
- IsNoetherianRingstatement and proof · cited by 268
- IsAlmostIntegralstatement · cited by 8
- IsIntegral.isAlmostIntegralproof · cited by 2
- IsAlmostIntegral.isIntegralproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- completeIntegralClosure_eq_integralClosureproof · cited by 0