Theorems · Theorem · commutative algebra
Submodule.FG.generators_ncard
∀ {R : Type u_1} {M : Type u} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {p : Submodule R M},
p.FG → p.generators.ncard = p.spanFinrank- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 94 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.
Cites19
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
- Set.Elemproof · cited by 7,166
- ENatproof · cited by 4,985
- Cardinalproof · cited by 2,598
- Set.ncardstatement and proof · cited by 344
- Submodule.FGstatement and proof · cited by 230
- ENat.toNatproof · cited by 143
- Cardinal.toENatproof · cited by 92
Cited by7
Results whose statement or proof uses this declaration.
- Ideal.height_le_height_add_spanFinrank_of_leproof · cited by 2
- Ideal.exists_finset_card_eq_height_of_isNoetherianRingproof · cited by 2
- Submodule.spanFinrank_eq_zero_iff_eq_botproof · cited by 1
- Submodule.spanFinrank_eq_one_iffproof · cited by 0