Theorems · Theorem · commutative algebra
emultiplicity_eq_of_dvd_of_not_dvd
∀ {α : Type u_1} [inst : Monoid α] {a b : α} {k : ℕ}, a ^ k ∣ b → ¬a ^ (k + 1) ∣ b → emultiplicity a b = ↑k- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- Monoidstatement and proof · cited by 3,887
- emultiplicitystatement · cited by 156
- Dvd.dvd.transproof · cited by 148
- FiniteMultiplicityproof · cited by 73
- pow_dvd_powproof · cited by 56
Cited by5
Results whose statement or proof uses this declaration.
- emultiplicity_eq_coeproof · cited by 9
- Ideal.emultiplicity_eq_emultiplicity_spanproof · cited by 3
- emultiplicity_add_of_gtproof · cited by 3
- emultiplicity_pow_selfproof · cited by 3
- multiplicity_eq_of_dvd_of_not_dvdproof · cited by 1