Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.associated_pow_irreducible
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [IsDiscreteValuationRing R] {x : R},
x ≠ 0 → ∀ {ϖ : R}, Irreducible ϖ → ∃ n, Associated x (ϖ ^ n)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 92 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.
- CommRingstatement and proof · cited by 17,173
- Multisetproof · cited by 2,627
- CommMonoidproof · cited by 2,264
- IsDomainstatement and proof · cited by 2,196
- Multiset.mapproof · cited by 876
- Multiset.prodproof · cited by 528
- Irreduciblestatement and proof · cited by 496
- Multiset.cardproof · cited by 375
- Associatedstatement and proof · cited by 296
- Associatesproof · cited by 210
- Associates.mkproof · cited by 137
- IsDiscreteValuationRingstatement and proof · cited by 117
Cited by4
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.eq_unit_mul_pow_irreducibleproof · cited by 6
- IsDiscreteValuationRing.addVal_eq_top_iffproof · cited by 4
- IsDiscreteValuationRing.addVal_le_iff_dvdproof · cited by 1
- IsDiscreteValuationRing.ideal_eq_span_pow_irreducibleproof · cited by 1