Theorems · Theorem · commutative algebra
AdicCompletion.algebraMap_isLocalHom_of_fg
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R],
(IsLocalRing.maximalIdeal R).FG → IsLocalHom (algebraMap R (AdicCompletion (IsLocalRing.maximalIdeal R) R))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Algebra.algebraMapstatement and proof · cited by 4,706
- Ideal.mapproof · cited by 692
- Ideal.comapproof · cited by 443
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- List.TFAE.outproof · cited by 177
- AdicCompletionstatement and proof · cited by 160
Cited by1
Results whose statement or proof uses this declaration.
- AdicCompletion.residueField_map_bijective_of_fgstatement · cited by 1