Theorems · Theorem · field theory
Field.finInsepDegree_mul_finInsepDegree_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], Field.finInsepDegree F E * Field.finInsepDegree E K = Field.finInsepDegree F K
If K / E / F is a field extension tower, such that E / F is algebraic, then their
inseparable degrees, as natural numbers, satisfy the tower law: $[E:F]_i [K:E]_i = [K:F]_i$.
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- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
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- Field.finInsepDegreestatement · cited by 15
- Field.lift_insepDegree_mul_lift_insepDegree_of_isAlgebraicproof · cited by 2
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