Theorems · Theorem · commutative algebra
IsLocalRing.residue_eq_zero_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R] (x : R),
(IsLocalRing.residue R) x = 0 ↔ x ∈ IsLocalRing.maximalIdeal R- Cited by
- 4 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- IsLocalRing.ResidueFieldstatement · cited by 156
- IsLocalRing.residuestatement · cited by 71
- RingHom.mem_kerproof · cited by 49
- IsLocalRing.ker_residueproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisor.of_map_ne_zeroproof · cited by 11
- Ideal.algebraMap_residueField_eq_zeroproof · cited by 5
- Algebra.FormallyUnramified.of_map_maximalIdealproof · cited by 1
- Localization.localRingHom_surjective_of_primesOver_eq_singletonproof · cited by 1