Theorems · Theorem · commutative algebra
FractionalIdeal.den_mem_inv
∀ {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] {I : FractionalIdeal (nonZeroDivisors R₁) K}, I ≠ ⊥ → (algebraMap R₁ K) ↑I.den ∈ I⁻¹- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Submoduleproof · cited by 7,192
- Idealproof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Algebra.algebraMapstatement · cited by 4,706
- Submonoidstatement · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- le_reflproof · cited by 2,061
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.num_le_mul_invproof · cited by 1