Theorems · Theorem · commutative algebra
multiplicity_eq_zero
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, multiplicity a b = 0 ↔ ¬a ∣ b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- multiplicitystatement · cited by 117
- zero_ne_oneproof · cited by 90
- emultiplicity_eq_zeroproof · cited by 8
- emultiplicity_eq_iff_multiplicity_eq_of_ne_oneproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- multiplicity_of_isUnit_rightproof · cited by 2
- Polynomial.rootMultiplicity_Cproof · cited by 1
- multiplicity_zero_eq_zero_of_ne_zeroproof · cited by 1