Theorems · Theorem · commutative algebra
Submodule.spanFinrank_singleton
∀ {R : Type u_1} {M : Type u} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {m : M},
m ≠ 0 → (R ∙ m).spanFinrank = 1- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- le_antisymmproof · cited by 2,068
- Submodule.spanstatement and proof · cited by 1,504
- le_transproof · cited by 985
- Submodule.spanFinrankstatement and proof · cited by 49
- Set.ncard_singletonproof · cited by 8
- Submodule.spanFinrank_span_le_ncard_of_finiteproof · cited by 5
- Submodule.fg_span_singletonproof · cited by 5
- Submodule.spanFinrank_eq_zero_iff_eq_botproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.spanFinrank_eq_one_iffproof · cited by 0