Theorems · Theorem · commutative algebra
IsLocalRing.map_maximalIdeal_lt_top
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : IsLocalRing R] [inst_2 : CommSemiring S]
[IsLocalRing S] (f : R →+* S) [IsLocalHom f], Ideal.map f (IsLocalRing.maximalIdeal R) < ⊤- Cited by
- 1 results in Mathlib
- Foundations
- Depth 49 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.
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Top.topstatement · cited by 9,680
- Idealstatement · cited by 4,748
- LE.le.trans_ltproof · cited by 795
- Ideal.mapstatement · cited by 692
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement · cited by 297
- IsLocalHomstatement and proof · cited by 100
- Ideal.IsMaximal.lt_topproof · cited by 3
- IsLocalRing.map_maximalIdeal_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.length_baseChangeproof · cited by 1