Theorems · Theorem · commutative algebra
FractionalIdeal.coe_inv_of_ne_zero
∀ (K : Type u_3) [inst : Field K] {R₁ : Type u_4} [inst_1 : CommRing R₁] [inst_2 : IsDomain R₁] [inst_3 : Algebra R₁ K]
[inst_4 : IsFractionRing R₁ K] {J : FractionalIdeal (nonZeroDivisors R₁) K},
J ≠ 0 → ↑J⁻¹ = IsLocalization.coeSubmodule K ⊤ / ↑J- Cited by
- 0 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- Idealstatement · cited by 4,748
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- FractionalIdealstatement and proof · cited by 423
- FractionalIdeal.coeToSubmodulestatement and proof · cited by 130
- IsLocalization.coeSubmodulestatement and proof · cited by 30
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