Theorems · Theorem · field theory
Polynomial.X_pow_sub_C_ne_zero
∀ {R : Type u} [inst : Ring R] [Nontrivial R] {n : ℕ}, 0 < n → ∀ (a : R), Polynomial.X ^ n - Polynomial.C a ≠ 0- Cited by
- 15 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingNontrivial
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 and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- sub_eq_add_negproof · cited by 1,023
- map_negproof · cited by 378
- Polynomial.X_pow_add_C_ne_zeroproof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- Polynomial.X_sub_C_ne_zeroproof · cited by 21
- Polynomial.mem_nthRootsproof · cited by 9
- minpoly.natSepDegree_eq_one_iff_pow_memproof · cited by 4
- isRoot_of_unity_iffproof · cited by 3
- Polynomial.card_nthRootsproof · cited by 3
- X_pow_sub_C_irreducible_of_primeproof · cited by 2
- gal_X_pow_sub_C_isSolvable_auxproof · cited by 1
- gal_X_pow_sub_one_isSolvableproof · cited by 1
- Polynomial.roots_cyclotomic_nodupproof · cited by 1
- IsCyclotomicExtension.splits_cyclotomicproof · cited by 1
- isSplittingField_X_pow_sub_C_of_root_adjoin_eq_topproof · cited by 1
- Field.isAlgebraic_of_adjoin_eq_adjoinproof · cited by 1