Theorems · Theorem · field theory
IsPurelyInseparable.insepDegree_eq
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [IsPurelyInseparable F E], Field.insepDegree F E = Module.rank F E
A purely inseparable extension has inseparable degree equal to degree.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Cardinalstatement and proof · cited by 2,598
- IntermediateFieldproof · cited by 988
- Module.rankstatement and proof · cited by 496
- IsPurelyInseparablestatement and proof · cited by 84
- Field.insepDegreestatement · cited by 23
- separableClosure.eq_bot_of_isPurelyInseparableproof · cited by 3
- IntermediateField.rank_bot'proof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsPurelyInseparable.finInsepDegree_eqproof · cited by 0