Theorems · Theorem · field theory
Field.lift_sepDegree_mul_lift_sepDegree_of_isAlgebraic
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type w) [inst_3 : Field K]
[inst_4 : Algebra F K] [inst_5 : Algebra E K] [IsScalarTower F E K] [Algebra.IsAlgebraic F E],
Cardinal.lift.{w, v} (Field.sepDegree F E) * Cardinal.lift.{v, w} (Field.sepDegree E K) =
Cardinal.lift.{v, w} (Field.sepDegree F K)If K / E / F is a field extension tower, such that E / F is algebraic, then their
separable degrees satisfy the tower law: $[E:F]_s [K:E]_s = [K:F]_s$.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- IsScalarTowerstatement and proof · cited by 3,896
- Cardinalstatement and proof · cited by 2,598
- Cardinal.liftstatement and proof · cited by 583
- Module.rankproof · cited by 496
- Algebra.IsAlgebraicstatement and proof · cited by 322
- separableClosureproof · cited by 55
- Field.sepDegreestatement and proof · cited by 24
- Field.lift_rank_mul_lift_sepDegree_of_isSeparableproof · cited by 2
- Field.sepDegree_eq_of_isPurelyInseparableproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Field.sepDegree_mul_sepDegree_of_isAlgebraicproof · cited by 1