Theorems · Definition · commutative algebra
Submodule.spanFinrank
{R : Type u_1} →
{M : Type u} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Submodule R M → ℕThe minimum cardinality of a generating set of a submodule as a natural number. If no finite
generating set exists, the span rank is defined to be 0.
- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 89 from the axioms · 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.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Cardinal.toNatproof · cited by 153
- Submodule.spanRankproof · cited by 61
Cited by51
Results whose statement or proof uses this declaration.
- Submodule.FG.generators_ncardstatement · cited by 7
- Submodule.spanFinrank_span_le_ncard_of_finitestatement · cited by 5
- Submodule.fg_iff_spanRank_eq_spanFinrankstatement · cited by 5
- Submodule.spanFinrank_span_le_encardstatement · cited by 4
- isRegularLocalRing_iffstatement and proof · cited by 4
- Ideal.height_le_height_add_spanFinrank_of_lestatement and proof · cited by 2
- IsRegularLocalRing.of_ringEquivproof · cited by 2
- Submodule.FG.spanRank_eq_spanFinrankstatement · cited by 2
- Submodule.FG.spanRank_le_iffstatement · cited by 2
- Submodule.spanFinrank_botstatement · cited by 2
- Submodule.spanFinrank_of_not_fgstatement · cited by 2
- Submodule.spanFinrank_subsingletonstatement and proof · cited by 2