Theorems · Definition · commutative algebra
Submodule.toAddSubmonoid
{R : Type u} →
{M : Type v} →
[inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Submodule R M → AddSubmonoid MReinterpret a Submodule as an AddSubmonoid.
- Defined in
- Mathlib.Algebra.Module.Submodule.Defs
- Cited by
- 162 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 30 definitions · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- AddSubmonoidstatement · cited by 1,178
Cited by229
Results whose statement or proof uses this declaration.
- Submodule.mapproof · cited by 614
- Submodule.comapproof · cited by 347
- Submodule.toAddSubgroupproof · cited by 106
- Submodule.prodproof · cited by 55
- Submodule.topologicalClosureproof · cited by 50
- LieSubmodule.mapproof · cited by 49
- Submodule.localized'proof · cited by 38
- NonUnitalAlgebra.adjoinproof · cited by 33
- Submodule.traceDualproof · cited by 26
- Ideal.comap_monoproof · cited by 25
- LieSubmodule.lie_memstatement · cited by 23
- LieSubmodule.comapproof · cited by 21
Showing the 200 most cited of 229.