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Theorems · Theorem · field theory

IsPurelyInseparable.HasExponent.has_exponent

∀ {K : Type u_2} {L : Type u_3} {inst : CommRing K} {inst_1 : Ring L} {inst_2 : Algebra K L}
  [self : IsPurelyInseparable.HasExponent K L], ∃ e, ∀ (a : L), a ^ ringExpChar K ^ e ∈ (algebraMap K L).range
Defined in
Mathlib.FieldTheory.PurelyInseparable.Exponent
Cited by
2 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
IsPurelyInseparable.HasExponent
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Around this declaration

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

IsPurelyInseparable.exponent · cited by 10IsPurelyInseparable.expon…IsPurelyInseparable.exponent_def · cited by 2IsPurelyInseparable.expon…IsPurelyInseparable.exponent_min · cited by 1IsPurelyInseparable.expon…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRing · cited by 7463RingAlgebra.algebraMap · cited by 4706Algebra.algebraMapSubring · cited by 602SubringRingHom.range · cited by 138RingHom.rangeringExpChar · cited by 27ringExpCharIsPurelyInseparable.HasExponent · cited by 13IsPurelyInseparable.HasEx…HasExponent.has_exponentCITED BYCITES

Cites8

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Cited by3

Results whose statement or proof uses this declaration.