Theorems · Theorem · commutative algebra
Ideal.irreducible_pow_sup_of_le
∀ {T : Type u_4} [inst : CommRing T] [IsDedekindDomain T] {I J : Ideal T},
Irreducible J → ∀ (n : ℕ), ↑n ≤ emultiplicity J I → J ^ n ⊔ I = J ^ n- Cited by
- 1 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.
Cites14
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.botproof · cited by 4,720
- IsDedekindDomainstatement and proof · cited by 668
- Irreduciblestatement and proof · cited by 496
- Multiset.countproof · cited by 302
- sup_of_le_leftproof · cited by 218
- emultiplicitystatement and proof · cited by 156
- UniqueFactorizationMonoid.normalizedFactorsproof · cited by 151
- min_eq_rightproof · cited by 54
- normalize_eqproof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- irreducible_pow_sup_of_leproof · cited by 0