Theorems · Definition · commutative algebra
Ideal.FG
{R : Type u_1} → [inst : Semiring R] → Ideal R → PropAn ideal of R is finitely generated if it is the span of a finite subset of R.
This is defeq to Submodule.FG, but unfolds more nicely.
- Defined in
- Mathlib.RingTheory.Finiteness.Defs
- Cited by
- 99 results in Mathlib
- Foundations
- Depth 54 from the axioms, rests on 916 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Ideal.spanproof · cited by 948
Cited by103
Results whose statement or proof uses this declaration.
- Algebra.FinitePresentation.equivproof · cited by 9
- Ideal.fg_of_isNoetherianRingstatement · cited by 9
- Algebra.FinitePresentation.transproof · cited by 8
- Ideal.FG.mapstatement and proof · cited by 7
- Algebra.FinitePresentation.ker_fG_of_surjectivestatement and proof · cited by 7
- Algebra.FinitePresentation.outstatement · cited by 6
- Ideal.isIdempotentElem_iff_of_fgstatement and proof · cited by 5
- AdicCompletion.pow_smul_top_eq_ker_evalstatement and proof · cited by 4
- Algebra.FinitePresentation.casesOnstatement and proof · cited by 4
- Ideal.exists_radical_pow_le_of_fgstatement and proof · cited by 4
- AdicCompletion.isLocalRing_of_fgstatement and proof · cited by 4
- AdicCompletion.maximalIdeal_eq_map_of_fgstatement and proof · cited by 3