Theorems · Theorem · commutative algebra
Ideal.irreducible_pow_sup
∀ {T : Type u_4} [inst : CommRing T] [inst_1 : IsDedekindDomain T] {I J : Ideal T},
I ≠ ⊥ →
Irreducible J → ∀ (n : ℕ), J ^ n ⊔ I = J ^ min (Multiset.count J (UniqueFactorizationMonoid.normalizedFactors I)) n- Cited by
- 5 results in Mathlib
- Foundations
- Depth 153 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
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Multisetproof · cited by 2,627
- IsDedekindDomainstatement and proof · cited by 668
- Multiset.prodproof · cited by 528
- Irreduciblestatement and proof · cited by 496
- Multiset.countstatement and proof · cited by 302
- pow_ne_zeroproof · cited by 208
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- Multiset.replicateproof · cited by 88
- Irreducible.ne_zeroproof · cited by 45
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.irreducible_pow_sup_of_geproof · cited by 2
- Ideal.irreducible_pow_sup_of_leproof · cited by 1
- Submodule.isInternal_prime_power_torsion_of_is_torsion_by_idealproof · cited by 1
- irreducible_pow_supproof · cited by 0
- Ideal.quotientToQuotientRangePowQuotSucc_surjectiveproof · cited by 0