Theorems · Theorem · field theory
Polynomial.separable_C
∀ {R : Type u} [inst : CommSemiring R] (r : R), (Polynomial.C r).Separable ↔ IsUnit r- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- IsUnitstatement and proof · cited by 1,602
- Polynomial.Cstatement and proof · cited by 1,598
- IsCoprimeproof · cited by 321
- Polynomial.Separablestatement · cited by 117
- Polynomial.derivative_Cproof · cited by 30
- Polynomial.isUnit_Cproof · cited by 19
- Polynomial.separable_defproof · cited by 7
- isCoprime_zero_rightproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.exists_separable_of_irreducibleproof · cited by 1