Theorems · Theorem · commutative algebra
FractionalIdeal.isNoetherian_zero
∀ {R₁ : Type u_3} [inst : CommRing R₁] {K : Type u_4} [inst_1 : Field K] [inst_2 : Algebra R₁ K], IsNoetherian R₁ ↥↑0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 7,192
- nonZeroDivisorsstatement · cited by 895
- FractionalIdealstatement · cited by 423
- Submodule.FGproof · cited by 230
- IsNoetherianstatement · cited by 208
- FractionalIdeal.coeToSubmodulestatement and proof · cited by 130
- le_bot_iffproof · cited by 116
- Submodule.fg_botproof · cited by 13
- FractionalIdeal.coe_zeroproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mulproof · cited by 1