Theorems · Theorem · commutative algebra
LocalSubring.range_toSubring
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : IsLocalRing R]
[inst_3 : Nontrivial S] (f : R →+* S), (LocalSubring.range f).toSubring = (Subring.map f ⊤).copy (Set.range ⇑f) ⋯- Cited by
- 0 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Top.topstatement · cited by 9,680
- Set.rangestatement · cited by 4,705
- Nontrivialstatement and proof · cited by 2,416
- Subringstatement · cited by 602
- IsLocalRingstatement and proof · cited by 339
- Subring.mapstatement · cited by 33
- LocalSubring.toSubringstatement and proof · cited by 18
- Subring.copystatement · cited by 7
- LocalSubring.rangestatement and proof · cited by 3
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