Theorems · Theorem · commutative algebra
IsIntegral.isAlmostIntegral
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsFractionRing R S]
{s : S}, IsIntegral R s → IsAlmostIntegral R s[Stacks Tag 00GX](https://stacks.math.columbia.edu/tag/00GX) (Part 2)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- le_rflproof · cited by 1,558
- nonZeroDivisorsproof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- IsIntegralstatement and proof · cited by 427
- IsAlmostIntegralstatement · cited by 8
- IsIntegral.isAlmostIntegral_of_isLocalizationproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- isAlmostIntegral_iff_isIntegralproof · cited by 1
- integralClosure_le_completeIntegralClosureproof · cited by 0