Theorems · Definition · commutative algebra
Submodule.FG
{R : Type u_1} →
{M : Type u_2} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Submodule R M → PropA submodule of M is finitely generated if it is the span of a finite subset of M.
- Defined in
- Mathlib.RingTheory.Finiteness.Defs
- Cited by
- 230 results in Mathlib
- Foundations
- Depth 54 from the axioms, rests on 874 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Submodule.spanproof · cited by 1,504
Cited by246
Results whose statement or proof uses this declaration.
- IsNoetherian.noetherianstatement · cited by 32
- Module.Finite.fg_topstatement · cited by 28
- Submodule.FG.mapstatement and proof · cited by 25
- Module.Flat.rTensor_preserves_injective_linearMapproof · cited by 24
- Module.Finite.iff_fgstatement · cited by 21
- Module.Finite.of_fgstatement · cited by 21
- LinearMap.HasFiniteRangeproof · cited by 20
- Submodule.fg_defstatement and proof · cited by 18
- Module.finite_defstatement · cited by 16
- IsIntegral.fg_adjoin_singletonstatement · cited by 13
- IsIntegral.of_mem_of_fgstatement and proof · cited by 13
- Submodule.fg_botstatement · cited by 13
Showing the 200 most cited of 246.