Theorems · Theorem · commutative algebra
FractionalIdeal.coeIdeal_finprod
∀ {R : Type u_1} [inst : CommRing R] (S : Submonoid R) (P : Type u_2) [inst_1 : CommRing P] [inst_2 : Algebra R P]
[IsLocalization S P] {α : Sort u_3} {f : α → Ideal R}, S ≤ nonZeroDivisors R → ↑(∏ᶠ (a : α), f a) = ∏ᶠ (a : α), ↑(f a)- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- Submonoidstatement and proof · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- IsLocalizationstatement and proof · cited by 636
- FractionalIdealstatement · cited by 423
- finprodstatement · cited by 257
- RingHom.toMonoidHomproof · cited by 132
- FractionalIdeal.coeIdealstatement · cited by 109
- FractionalIdeal.coeIdealHomproof · cited by 3
- FractionalIdeal.coeIdeal_injective'proof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.finprod_heightOneSpectrum_factorization_coeproof · cited by 1