Theorems · Theorem · commutative algebra
IsLocalRing.map_maximalIdeal_of_surjective
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : IsLocalRing R]
[inst_3 : IsLocalRing S] (f : R →+* S),
Function.Surjective ⇑f → Ideal.map f (IsLocalRing.maximalIdeal R) = IsLocalRing.maximalIdeal S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Ideal.mapstatement and proof · cited by 692
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- IsLocalHomproof · cited by 100
- Ideal.map_comap_of_surjectiveproof · cited by 13
- IsLocalHom.of_surjectiveproof · cited by 4
- IsLocalRing.maximalIdeal_comapproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.map_ringEquiv_maximalIdealproof · cited by 1