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Theorems · Theorem · commutative algebra

IsLocalRing.ker_residue

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R],
  RingHom.ker (IsLocalRing.residue R) = IsLocalRing.maximalIdeal R
Defined in
Mathlib.RingTheory.LocalRing.ResidueField.Basic
Cited by
1 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsLocalRing
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Around this declaration

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

IsLocalRing.residue_eq_zero_iff · cited by 4IsLocalRing.residue_eq_ze…CommRing · cited by 17173CommRingRingHom · cited by 10189RingHomIdeal · cited by 4748IdealRingHom.ker · cited by 363RingHom.kerIsLocalRing · cited by 339IsLocalRingIsLocalRing.maximalIdeal · cited by 297IsLocalRing.maximalIdealIsLocalRing.ResidueField · cited by 156IsLocalRing.ResidueFieldIsLocalRing.residue · cited by 71IsLocalRing.residueIdeal.mk_ker · cited by 59Ideal.mk_kerIsLocalRing.ker_residueCITED BYCITES

Cites9

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Cited by1

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