Theorems · Theorem · commutative algebra
Submodule.spanFinrank_subsingleton
∀ {R : Type u_1} {M : Type u} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Subsingleton R]
(p : Submodule R M), p.spanFinrank = 0- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Submodule.spanFinrankstatement and proof · cited by 49
- Module.subsingletonproof · cited by 20
- Submodule.eq_bot_of_subsingletonproof · cited by 5
- Submodule.spanFinrank_botproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ringKrullDim_le_ringKrullDim_quotient_add_spanFinrankproof · cited by 2