Theorems · Theorem · commutative algebra
isRelPrime_iff_isCoprime
∀ {R : Type u} [inst : CommRing R] {x y : R} [Submodule.IsPrincipal (Ideal.span {x, y})], IsRelPrime x y ↔ IsCoprime x y- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 1 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.
Cites8
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
- Ideal.spanstatement and proof · cited by 948
- IsCoprimestatement · cited by 321
- IsRelPrimestatement · cited by 136
- Submodule.IsPrincipalstatement and proof · cited by 129
- IsRelPrime.isCoprimeproof · cited by 5
- IsCoprime.isRelPrimeproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Irreducible.coprime_iff_not_dvdproof · cited by 5