Theorems · Theorem · commutative algebra
FractionalIdeal.isNoetherian_coeIdeal
∀ {R₁ : Type u_3} [inst : CommRing R₁] {K : Type u_4} [inst_1 : Field K] [inst_2 : Algebra R₁ K] [IsNoetherianRing R₁]
(I : Ideal R₁), IsNoetherian R₁ ↥↑↑I- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- le_transproof · cited by 985
- nonZeroDivisorsstatement and proof · cited by 895
- FractionalIdealproof · cited by 423
- IsNoetherianRingstatement and proof · cited by 268
- IsNoetherianstatement · cited by 208
- Algebra.linearMapproof · cited by 157
- FractionalIdeal.coeToSubmodulestatement · cited by 130
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.isNoetherianproof · cited by 1