Theorems · Theorem · commutative algebra
IsLocalization.integerNormalization_eq_zero_iff
∀ {R : Type u_1} [inst : CommRing R] {M : Submonoid R} {S : Type u_2} [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : IsLocalization M S] [IsDomain R],
M ≤ nonZeroDivisors R → ∀ (p : Polynomial S), IsLocalization.integerNormalization M p = 0 ↔ p = 0- Defined in
- Mathlib.RingTheory.Localization.Integral
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- Polynomial.mapproof · cited by 806
- IsLocalizationstatement and proof · cited by 636
- FaithfulSMulproof · cited by 340
- Polynomial.mapRingHomproof · cited by 98
Cited by1
Results whose statement or proof uses this declaration.
- IsFractionRing.integerNormalization_eq_zero_iffproof · cited by 2