Theorems · Theorem · field theory
Polynomial.irreducible_of_degree_eq_one_of_isRelPrime_coeff
∀ {R : Type u} [inst : CommRing R] [IsDomain R] {p : Polynomial R},
p.degree = 1 → IsRelPrime (p.coeff 0) (p.coeff 1) → Irreducible pA degree 1 polynomial C a * X + C b is irreducible
if a, b are relatively prime.
- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- LT.lt.leproof · cited by 2,189
- IsUnitproof · cited by 1,602
- Polynomial.Cproof · cited by 1,598
- WithBotstatement and proof · cited by 1,498
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.degreestatement and proof · cited by 643
- Irreduciblestatement · cited by 496
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.irreducible_C_mul_X_add_Cproof · cited by 2