Theorems · Theorem · commutative algebra
dvd_or_isCoprime
∀ {R : Type u} [inst : CommRing R] [IsBezout R] (x y : R), Irreducible x → x ∣ y ∨ IsCoprime x y- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 2 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.
Cites6
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
- Irreduciblestatement and proof · cited by 496
- IsCoprimestatement · cited by 321
- IsBezoutstatement and proof · cited by 23
- IsRelPrime.isCoprimeproof · cited by 5
- Irreducible.dvd_or_isRelPrimeproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanDomain.dvd_or_coprimeproof · cited by 1
- IsPrimitiveRoot.minpoly_eq_powproof · cited by 1