Theorems · Theorem · field theory
Field.finSepDegree_eq_finrank_iff
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [FiniteDimensional F E], Field.finSepDegree F E = Module.finrank F E ↔ Algebra.IsSeparable F E
If E / F is a finite extension, then its separable degree is equal to its degree if and
only if it is a separable extension.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- le_antisymmproof · cited by 2,068
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- le_of_not_gtproof · cited by 430
- IntermediateField.adjoinproof · cited by 382
- neg_neg_of_posproof · cited by 227
- Algebra.IsSeparablestatement and proof · cited by 210
- neg_eq_zeroproof · cited by 171
- IsAlgebraicproof · cited by 163
- sub_eq_zero_of_eqproof · cited by 154
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.isSeparable_adjoin_simple_iff_isSeparableproof · cited by 4
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3