Mathlib Map

Theorems · Theorem · field theory

IsPRadical.ker_le

∀ {K : Type u_1} {L : Type u_2} [inst : CommSemiring K] [inst_1 : CommSemiring L] (i : K →+* L) (p : ℕ)
  [IsPRadical i p], RingHom.ker i ≤ pNilradical K p
Defined in
Mathlib.FieldTheory.IsPerfectClosure
Cited by
3 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringCommSemiringIsPRadical
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

PerfectRing.liftAux_apply · cited by 2PerfectRing.liftAux_applyIsPRadical.comap_pNilradical · cited by 1IsPRadical.comap_pNilradi…IsPRadical.trans · cited by 0IsPRadical.transCommSemiring · cited by 10911CommSemiringRingHom · cited by 10189RingHomIdeal · cited by 4748IdealRingHom.ker · cited by 363RingHom.kerIsPRadical · cited by 34IsPRadicalpNilradical · cited by 18pNilradicalIsPRadical.ker_le' · cited by 2IsPRadical.ker_le'IsPRadical.ker_leCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.