Theorems · Theorem · commutative algebra
FractionalIdeal.ringEquivOfRingEquiv_apply_val
∀ {R : Type u_5} {S : Type u_6} (K : Type u_7) (L : Type u_8) [inst : CommRing R] [inst_1 : IsDomain R]
[inst_2 : CommRing S] [inst_3 : IsDomain S] [inst_4 : CommRing K] [inst_5 : CommRing L] [inst_6 : Algebra R K]
[inst_7 : Algebra S L] [inst_8 : IsFractionRing R K] [inst_9 : IsFractionRing S L] (f : R ≃+* S)
(I : FractionalIdeal (nonZeroDivisors R) K),
↑((FractionalIdeal.ringEquivOfRingEquiv K L f) I) =
Submodule.map ↑(IsFractionRing.semilinearEquivOfRingEquiv K L f) ↑I- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
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
- Algebrastatement and proof · cited by 11,388
- Submodulestatement · cited by 7,192
- IsDomainstatement and proof · cited by 2,196
- LinearEquiv.toLinearMapstatement · cited by 1,171
- RingEquivstatement and proof · cited by 1,147
- nonZeroDivisorsstatement and proof · cited by 895
- RingHomClass.toRingHomstatement · cited by 746
- IsFractionRingstatement and proof · cited by 738
- Submodule.mapstatement · cited by 614
- RingEquiv.symmstatement · cited by 567
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