Theorems · Definition · commutative algebra
IsCoprime
{R : Type u} → [CommSemiring R] → R → R → PropThe proposition that x and y are coprime, defined to be the existence of a and b such
that a * x + b * y = 1. Note that elements with no common divisors are not necessarily coprime,
e.g., the multivariate polynomials x₁ and x₂ are not coprime.
- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 321 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 98 definitions · uses no axioms
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
Cited by331
Results whose statement or proof uses this declaration.
- Polynomial.Separableproof · cited by 117
- IsCoprime.symmstatement and proof · cited by 22
- isCoprime_commstatement · cited by 17
- Int.isCoprime_iff_gcd_eq_onestatement and proof · cited by 16
- Ideal.isCoprime_iff_sup_eqstatement · cited by 10
- Ideal.quotientMulEquivQuotientProdstatement and proof · cited by 8
- IsCoprime.of_mul_left_leftstatement and proof · cited by 8
- isCoprime_one_leftstatement · cited by 8
- Polynomial.separable_defstatement · cited by 7
- IsCoprime.powstatement and proof · cited by 7
- Polynomial.separable_mapproof · cited by 6
- Ideal.quotientInfRingEquivPiQuotientstatement and proof · cited by 6
Showing the 200 most cited of 331.