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Theorems · Theorem · commutative algebra

WfDvdMonoid.max_power_factor

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [WfDvdMonoid α] {a₀ x : α},
  a₀ ≠ 0 → Irreducible x → ∃ n a, ¬x ∣ a ∧ a₀ = x ^ n * a
Defined in
Mathlib.RingTheory.UniqueFactorizationDomain.Multiplicity
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroWfDvdMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RatFunc.valuation_eq_valuation_uniformizingPolynomial_pow_of_valuation_X_le_one · cited by 2RatFunc.valuation_eq_valu…exists_reduced_fraction' · cited by 1exists_reduced_fraction'CommMonoidWithZero · cited by 913CommMonoidWithZeroIrreducible · cited by 496IrreducibleIrreducible.not_isUnit · cited by 42Irreducible.not_isUnitWfDvdMonoid · cited by 37WfDvdMonoidWfDvdMonoid.max_power_factor' · cited by 2WfDvdMonoid.max_power_fac…WfDvdMonoid.max_power_factorCITED BYCITES

Cites5

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Cited by2

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