Theorems · Theorem · commutative algebra
FractionalIdeal.spanFinset_eq_zero
∀ {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] {ι : Type u_5} {s : Finset ι} {f : ι → K},
FractionalIdeal.spanFinset R₁ s f = 0 ↔ ∀ j ∈ s, f j = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Finsetstatement and proof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.imageproof · cited by 5,609
- Submodule.spanproof · cited by 1,504
- nonZeroDivisorsstatement · cited by 895
- IsFractionRingstatement and proof · cited by 738
- FractionalIdealstatement · cited by 423
- FractionalIdeal.coe_zeroproof · cited by 10
- FractionalIdeal.spanFinsetstatement · cited by 5
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