Theorems · Definition · commutative algebra
Submodule.toSubMulAction
{R : Type u} →
{M : Type v} →
[inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Submodule R M → SubMulAction R MReinterpret a Submodule as a SubMulAction.
- Defined in
- Mathlib.Algebra.Module.Submodule.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddSubmonoid.toAddSubsemigroupproof · cited by 198
- AddSubsemigroup.carrierproof · cited by 198
- Submodule.toAddSubmonoidproof · cited by 162
- SubMulActionstatement · cited by 120
- Submodule.smul_mem'proof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- Submodule.smul_mem_iffproof · cited by 19
- Submodule.smul_of_tower_memproof · cited by 11
- Submodule.smul_mem_iff'proof · cited by 2
- Submodule.toSubMulAction_injstatement · cited by 1
- Submodule.toSubMulAction_injectivestatement and proof · cited by 1
- Submodule.toSubMulAction_strictMonostatement · cited by 1
- Submodule.coe_toSubMulActionstatement · cited by 0
- Submodule.toSubMulAction_monostatement · cited by 0
- Submodule.toSubMulAction_onestatement and proof · cited by 0