Theorems · Theorem · commutative algebra
FractionalIdeal.one_div_spanSingleton
∀ {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] (x : K),
1 / FractionalIdeal.spanSingleton (nonZeroDivisors R₁) x = FractionalIdeal.spanSingleton (nonZeroDivisors R₁) x⁻¹- Cited by
- 2 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.
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
- Fieldstatement and proof · cited by 7,404
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- FractionalIdealstatement · cited by 423
- mul_inv_cancel₀proof · cited by 210
- inv_zeroproof · cited by 184
- FractionalIdeal.spanSingletonstatement and proof · cited by 73
- FractionalIdeal.spanSingleton_oneproof · cited by 12
- FractionalIdeal.spanSingleton_mul_spanSingletonproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- FractionalIdeal.div_spanSingletonproof · cited by 4
- FractionalIdeal.spanSingleton_invproof · cited by 1