Theorems · Theorem · commutative algebra
Ideal.fg_of_isNoetherianRing
∀ {R : Type u_1} [inst : Semiring R] [IsNoetherianRing R] (I : Ideal R), I.FG- Defined in
- Mathlib.RingTheory.Noetherian.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIsNoetherianRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- IsNoetherianRingstatement and proof · cited by 268
- Ideal.FGstatement · cited by 99
- IsNoetherian.noetherianproof · cited by 32
Cited by9
Results whose statement or proof uses this declaration.
- AdicCompletion.maximalIdeal_eq_mapproof · cited by 2
- AdicCompletion.residueField_map_bijectiveproof · cited by 1
- AdicCompletion.mem_maximalIdeal_iff_eval_one_eq_zeroproof · cited by 1
- IsLocalRing.spanFinrank_maximalIdeal_eq_finrank_cotangentSpaceproof · cited by 1
- Submodule.exists_eq_colon_of_mem_minimalPrimesproof · cited by 1
- IsLocalRing.rank_cotangentSpace_eq_spanrank_maximalIdealproof · cited by 0
- Ideal.FG.of_isNoetherianRingproof · cited by 0
- AdicCompletion.spanFinrank_maximalIdeal_eqproof · cited by 0