Theorems · Theorem · commutative algebra
FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul
∀ {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] [IsDomain R₁] (x : R₁) {I : FractionalIdeal (nonZeroDivisors R₁) K},
IsNoetherian R₁ ↥↑I →
IsNoetherian R₁ ↥↑(FractionalIdeal.spanSingleton (nonZeroDivisors R₁) ((algebraMap R₁ K) x)⁻¹ * I)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_oneproof · cited by 3,885
- IsDomainstatement and proof · cited by 2,196
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.isNoetherianproof · cited by 1