Theorems · Theorem · commutative algebra
FractionalIdeal.map_div
∀ {R₁ : Type u_3} [inst : CommRing R₁] {K : Type u_4} [inst_1 : Field K] [inst_2 : Algebra R₁ K]
[inst_3 : IsFractionRing R₁ K] [inst_4 : IsDomain R₁] {K' : Type u_5} [inst_5 : Field K'] [inst_6 : Algebra R₁ K']
[inst_7 : IsFractionRing R₁ K'] (I J : FractionalIdeal (nonZeroDivisors R₁) K) (h : K ≃ₐ[R₁] K'),
FractionalIdeal.map (↑h) (I / J) = FractionalIdeal.map (↑h) I / FractionalIdeal.map (↑h) J- Cited by
- 2 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgHomproof · cited by 3,236
- IsDomainstatement and proof · cited by 2,196
- AlgEquivstatement and proof · cited by 1,681
- LinearEquiv.toLinearMapproof · cited by 1,171
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- Submodule.mapproof · cited by 614
- FractionalIdealstatement and proof · cited by 423
- AlgEquiv.toAlgHomstatement and proof · cited by 273
Cited by2
Results whose statement or proof uses this declaration.
- FractionalIdeal.map_one_divproof · cited by 0
- FractionalIdeal.map_invproof · cited by 0