Theorems · Theorem · commutative algebra
exists_associated_pow_of_associated_pow_mul
∀ {R : Type u} [inst : CommRing R] [IsBezout R] [IsDomain R] {a b c : R},
IsCoprime a b → ∀ {k : ℕ}, Associated (c ^ k) (a * b) → ∃ d, Associated (d ^ k) a- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Unitsproof · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- IsCoprimestatement and proof · cited by 321
- Associatedstatement and proof · cited by 296
- Units.isUnitproof · cited by 116
- Associated.symmproof · cited by 87
- IsBezoutstatement and proof · cited by 23
- exists_associated_pow_of_mul_eq_pow'proof · cited by 2
- isCoprime_mul_unit_right_rightproof · cited by 2
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