Theorems · Theorem · commutative algebra
IsLocalRing.of_surjective
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [IsLocalRing R] [inst_2 : Semiring S] [Nontrivial S]
(f : R →+* S) [IsLocalHom f], Function.Surjective ⇑f → IsLocalRing S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Nontrivialstatement and proof · cited by 2,416
- IsUnitproof · cited by 1,602
- map_addproof · cited by 964
- IsLocalRingstatement and proof · cited by 339
- IsLocalHomstatement and proof · cited by 100
- RingHom.isUnit_mapproof · cited by 14
- IsLocalHom.map_nonunitproof · cited by 8
- IsLocalRing.isUnit_or_isUnit_of_isUnit_addproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- RingEquiv.isLocalRingproof · cited by 2