Theorems · Definition · ring theory
skewAdjoint.submodule
(R : Type u_1) →
(A : Type u_2) →
[inst : Semiring R] →
[inst_1 : StarMul R] →
[TrivialStar R] →
[inst_3 : AddCommGroup A] →
[inst_4 : Module R A] → [inst_5 : StarAddMonoid A] → [StarModule R A] → Submodule R AThe skew-adjoint elements of a star module, as a submodule.
- Defined in
- Mathlib.Algebra.Star.Module
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement · cited by 7,192
- AddSubgroupproof · cited by 3,232
- StarModulestatement and proof · cited by 570
- StarAddMonoidstatement and proof · cited by 296
- StarMulstatement and proof · cited by 195
- AddSubgroup.toAddSubmonoidproof · cited by 91
- TrivialStarstatement and proof · cited by 66
- skewAdjointproof · cited by 34
Cited by5
Results whose statement or proof uses this declaration.
- StarModule.decomposeProdAdjointproof · cited by 4
- selfAdjointPart_comp_subtype_skewAdjointstatement and proof · cited by 0
- StarModule.decomposeProdAdjointL_symm_applystatement · cited by 0
- StarModule.decomposeProdAdjoint_symm_applystatement · cited by 0
- skewAdjointPart_comp_subtype_skewAdjointstatement and proof · cited by 0