Theorems · Theorem · field theory
Polynomial.irreducible_X_sub_C
∀ {R : Type u} [inst : CommRing R] [IsDomain R] (r : R), Irreducible (Polynomial.X - Polynomial.C r)- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- Irreduciblestatement · cited by 496
- Prime.irreducibleproof · cited by 54
- Polynomial.prime_X_sub_Cproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- X_pow_sub_C_irreducible_of_oddproof · cited by 3
- Polynomial.cyclotomic_irreducible_pow_of_irreducible_powproof · cited by 2
- minpoly.rootproof · cited by 1
- Ideal.IsField.of_isPrincipalIdealRing_polynomialproof · cited by 0