Theorems · Theorem · commutative algebra
IsLocalRing.maximalIdeal_comap
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : IsLocalRing R] [inst_2 : CommSemiring S]
[inst_3 : IsLocalRing S] (f : R →+* S) [IsLocalHom f],
Ideal.comap f (IsLocalRing.maximalIdeal S) = IsLocalRing.maximalIdeal R- Cited by
- 3 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
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.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Idealstatement · cited by 4,748
- Ideal.mapproof · cited by 692
- Ideal.comapstatement and proof · cited by 443
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- List.TFAE.outproof · cited by 177
- IsLocalHomstatement and proof · cited by 100
Cited by3
Results whose statement or proof uses this declaration.
- IsLocalRing.map_maximalIdeal_leproof · cited by 1
- IsLocalRing.map_maximalIdeal_of_surjectiveproof · cited by 1
- AdicCompletion.spanFinrank_maximalIdeal_eqproof · cited by 0