Theorems · Theorem · commutative algebra
FiniteMultiplicity.not_pow_dvd_of_multiplicity_lt
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, FiniteMultiplicity a b → ∀ {m : ℕ}, multiplicity a b < m → ¬a ^ m ∣ b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 35 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.
- ENatproof · cited by 4,985
- Monoidstatement and proof · cited by 3,887
- multiplicitystatement and proof · cited by 117
- FiniteMultiplicitystatement and proof · cited by 73
- FiniteMultiplicity.emultiplicity_eq_multiplicityproof · cited by 31
- not_pow_dvd_of_emultiplicity_ltproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- multiplicity_mulproof · cited by 5
- Ideal.emultiplicity_eq_emultiplicity_spanproof · cited by 3
- emultiplicity_add_of_gtproof · cited by 3
- multiplicity_pos_of_dvdproof · cited by 2
- Polynomial.eval_divByMonic_pow_rootMultiplicity_ne_zeroproof · cited by 2