Theorems · Theorem · commutative algebra
FractionalIdeal.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] (J : FractionalIdeal (nonZeroDivisors R₁) K) (d : K),
J / FractionalIdeal.spanSingleton (nonZeroDivisors R₁) d = FractionalIdeal.spanSingleton (nonZeroDivisors R₁) d⁻¹ * J- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- Submoduleproof · cited by 7,192
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- IsDomainstatement and proof · cited by 2,196
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- nonZeroDivisorsstatement and proof · cited by 895
Cited by4
Results whose statement or proof uses this declaration.
- FractionalIdeal.count_well_definedproof · cited by 5
- FractionalIdeal.finprod_heightOneSpectrum_factorizationproof · cited by 2
- FractionalIdeal.spanSingleton_div_spanSingletonproof · cited by 1
- FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mulproof · cited by 1