Theorems · Theorem · commutative algebra
isCoprime_of_dvd
∀ {R : Type u} [inst : CommRing R] [IsBezout R] (x y : R),
¬(x = 0 ∧ y = 0) → (∀ z ∈ nonunits R, z ≠ 0 → z ∣ x → ¬z ∣ y) → IsCoprime x y- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- IsCoprimestatement · cited by 321
- nonunitsstatement and proof · cited by 35
- IsBezoutstatement and proof · cited by 23
- IsRelPrime.isCoprimeproof · cited by 5
- isRelPrime_of_no_nonunits_factorsproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- EuclideanDomain.isCoprime_of_dvdproof · cited by 2
- Polynomial.isCoprime_iff_aeval_ne_zeroproof · cited by 0
- Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosedproof · cited by 0
- Zsqrtd.isCoprime_of_dvd_isCoprimeproof · cited by 0