Theorems · Theorem · field theory
Algebra.IsAlgebraic.perfectField
∀ (K : Type u_1) {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [Algebra.IsAlgebraic K L]
[PerfectField K], PerfectField LIf L / K is an algebraic extension, K is a perfect field, then so is L.
- Defined in
- Mathlib.FieldTheory.Perfect
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Polynomial.mapproof · cited by 806
- Irreducibleproof · cited by 496
- Polynomial.Monicproof · cited by 461
- Algebra.IsAlgebraicstatement and proof · cited by 322
- PerfectFieldstatement and proof · cited by 36
- Polynomial.Separable.of_dvdproof · cited by 14
- Polynomial.Separable.mapproof · cited by 14
- Irreducible.exists_dvd_monic_irreducible_of_isIntegralproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- PerfectField.of_ringEquivproof · cited by 0