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Theorems · Definition · field theory

RingHom.IsPurelyInseparable

{F : Type u} → {E : Type v} → [inst : CommRing F] → [inst_1 : CommRing E] → (F →+* E) → Prop

A ring homomorphism f : F →+* E is purely inseparable if E is purely inseparable as an F-algebra.

Defined in
Mathlib.RingTheory.RingHom.PurelyInseparable
Cited by
5 results in Mathlib
Foundations
Depth 19 from the axioms · uses no axioms
Assumes
CommRingCommRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

RingHom.IsPurelyInseparable.id · cited by 1IsPurelyInseparable.idRingHom.isPurelyInseparable_algebraMap_iff · cited by 0RingHom.isPurelyInseparab…AlgebraicGeometry.tfae_universallyInjective · cited by 0AlgebraicGeometry.tfae_un…RingHom.IsPurelyInseparable.comp · cited by 0IsPurelyInseparable.compRingHom.IsPurelyInseparable.containsIdentities · cited by 0IsPurelyInseparable.conta…CommRing · cited by 17173CommRingRingHom · cited by 10189RingHomIsPurelyInseparable · cited by 84IsPurelyInseparableRingHom.IsPurelyInseparableCITED BYCITES

Cites3

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Cited by5

Results whose statement or proof uses this declaration.