Theorems · Theorem · commutative algebra
IsRelPrime.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
- 5 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Top.topproof · cited by 9,680
- Idealproof · cited by 4,748
- Ideal.spanstatement and proof · cited by 948
- IsCoprimestatement · cited by 321
- IsRelPrimestatement and proof · cited by 136
- Submodule.IsPrincipalstatement and proof · cited by 129
- Set.singleton_unionproof · cited by 22
- IsBezout.gcdproof · cited by 12
- Ideal.span_unionproof · cited by 11
- Ideal.isCoprime_iff_sup_eqproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- isCoprime_of_dvdproof · cited by 4
- isCoprime_of_irreducible_dvdproof · cited by 3
- OnePoint.exists_mem_SL2proof · cited by 2
- dvd_or_isCoprimeproof · cited by 2
- isRelPrime_iff_isCoprimeproof · cited by 1