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Theorems · Theorem · field theory

IsPurelyInseparable.elemExponent_min

∀ {K : Type u_2} {L : Type u_3} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
  [inst_3 : IsPurelyInseparable K L] {a : L} {n : ℕ},
  n < IsPurelyInseparable.elemExponent K a → a ^ ringExpChar K ^ n ∉ (algebraMap K L).range
Defined in
Mathlib.FieldTheory.PurelyInseparable.Exponent
Cited by
1 results in Mathlib
Foundations
Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebraIsPurelyInseparable
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsPurelyInseparable.elemExponent_min' · cited by 0IsPurelyInseparable.elemE…Algebra · cited by 11388AlgebraField · cited by 7404FieldAlgebra.algebraMap · cited by 4706Algebra.algebraMapSubring · cited by 602SubringRingHom.range · cited by 138RingHom.rangeIsPurelyInseparable · cited by 84IsPurelyInseparableringExpChar · cited by 27ringExpCharIsPurelyInseparable.elemExponent · cited by 15IsPurelyInseparable.elemE…IsPurelyInseparable.elemExponent_le_of_pow_mem · cited by 3IsPurelyInseparable.elemE…IsPurelyInseparable.elemExpon…CITED BYCITES

Cites9

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Cited by1

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