Theorems · Theorem · commutative algebra
Ideal.irreducible_pow_sup_of_ge
∀ {T : Type u_4} [inst : CommRing T] [IsDedekindDomain T] {I J : Ideal T},
I ≠ ⊥ → Irreducible J → ∀ (n : ℕ), emultiplicity J I ≤ ↑n → J ^ n ⊔ I = J ^ multiplicity J I- Cited by
- 2 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDedekindDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- LE.le.trans_ltproof · cited by 795
- IsDedekindDomainstatement and proof · cited by 668
- Irreduciblestatement and proof · cited by 496
- Multiset.countproof · cited by 302
- emultiplicitystatement and proof · cited by 156
- UniqueFactorizationMonoid.normalizedFactorsproof · cited by 151
- multiplicitystatement and proof · cited by 117
- Nat.cast_injproof · cited by 70
Cited by2
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.exists_intValuation_mul_sub_ltproof · cited by 1
- irreducible_pow_sup_of_geproof · cited by 0