Theorems · Definition · field theory
IsPurelyInseparable.exponent
(K : Type u_2) →
(L : Type u_3) →
[inst : CommRing K] → [inst_1 : Ring L] → [inst_2 : Algebra K L] → [IsPurelyInseparable.HasExponent K L] → ℕThe exponent of a purely inseparable extension is the smallest
natural number e such that a ^ ringExpChar K ^ e ∈ K for all a ∈ L.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Nat.findproof · cited by 139
- IsPurelyInseparable.HasExponentstatement and proof · cited by 13
- IsPurelyInseparable.HasExponent.has_exponentproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- IsPurelyInseparable.iterateFrobeniusₛₗstatement and proof · cited by 3
- IsPurelyInseparable.iterateFrobeniusstatement and proof · cited by 2
- IsPurelyInseparable.algebraMap_iterateFrobeniusstatement and proof · cited by 2
- IsPurelyInseparable.exponent_defstatement · cited by 2
- IsPurelyInseparable.iterateFrobenius_algebraMapstatement and proof · cited by 1
- IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗstatement and proof · cited by 1
- IsPurelyInseparable.exponent_minstatement and proof · cited by 1
- IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMapstatement and proof · cited by 0
- IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_basestatement and proof · cited by 0
- IsPurelyInseparable.elemExponent_le_exponentstatement · cited by 0
- IsPurelyInseparable.exponent_def'statement · cited by 0
- IsPurelyInseparable.exponent_min'statement and proof · cited by 0