Theorems · Definition · commutative algebra
WfDvdMonoid
(α : Type u_2) → [CommMonoidWithZero α] → Prop
Well-foundedness of the strict version of ∣, which is equivalent to the descending chain condition on divisibility and to the ascending chain condition on principal ideals in an integral domain.
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- DvdNotUnitproof · cited by 33
- IsWellFoundedproof · cited by 18
Cited by37
Results whose statement or proof uses this declaration.
- WfDvdMonoid.exists_irreducible_factorstatement and proof · cited by 12
- wellFounded_dvdNotUnitstatement and proof · cited by 7
- FiniteMultiplicity.of_prime_leftstatement and proof · cited by 5
- WfDvdMonoid.exists_factorsstatement and proof · cited by 5
- WfDvdMonoid.induction_on_irreduciblestatement and proof · cited by 5
- UniqueFactorizationMonoid.of_exists_prime_factorsproof · cited by 4
- IsDiscreteValuationRing.associated_pow_irreducibleproof · cited by 4
- Ideal.isPrincipal_of_isPrincipal_isLocalizationAway_of_primestatement and proof · cited by 2
- IsBezout.TFAEstatement and proof · cited by 2
- WfDvdMonoid.isRelPrime_of_no_irreducible_factorsstatement and proof · cited by 2
- WfDvdMonoid.max_power_factorstatement and proof · cited by 2
- WfDvdMonoid.max_power_factor'statement and proof · cited by 2