Theorems · Theorem · field theory
PerfectField.separable_iff_squarefree
∀ {K : Type u_1} [inst : Field K] [PerfectField K] {g : Polynomial K}, g.Separable ↔ Squarefree g- Defined in
- Mathlib.FieldTheory.Perfect
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldPerfectField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Irreducibleproof · cited by 496
- Polynomial.derivativeproof · cited by 331
- Polynomial.Separablestatement · cited by 117
- Squarefreestatement and proof · cited by 112
- dvd_mul_rightproof · cited by 89
- Irreducible.not_isUnitproof · cited by 42
- PerfectFieldstatement and proof · cited by 36
- Polynomial.derivative_mulproof · cited by 35
- mul_dvd_mul_leftproof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- Module.End.exists_isNilpotent_isSemisimpleproof · cited by 3
- Module.End.IsSemisimple.of_mem_adjoin_pairproof · cited by 3