Theorems · Theorem · ring theory
SetLike.algebraMap_mem_graded
∀ {ι : Type u_1} {S : Type u_3} {R : Type u_4} [inst : Zero ι] [inst_1 : CommSemiring S] [inst_2 : Semiring R]
[inst_3 : Algebra S R] (A : ι → Submodule S R) [SetLike.GradedOne A] (s : S), (algebraMap S R) s ∈ A 0- Defined in
- Mathlib.Algebra.DirectSum.Internal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 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.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Submodulestatement and proof · cited by 7,192
- Algebra.algebraMapstatement · cited by 4,706
- Submodule.smul_memproof · cited by 204
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
- SetLike.GradedOnestatement and proof · cited by 7
- SetLike.one_mem_gradedproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- CliffordAlgebra.even_inductionstatement and proof · cited by 3
- CliffordAlgebra.even.lift.aux_mulproof · cited by 0