Theorems · Definition · ring theory
AddMonoidAlgebra.gradeBy
{M : Type u_1} →
{ι : Type u_2} → (R : Type u_3) → [inst : CommSemiring R] → (M → ι) → ι → Submodule R (AddMonoidAlgebra R M)The submodule corresponding to each grade given by the degree function f.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Grading
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Finsupp.supportproof · cited by 828
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidAlgebra.coeffproof · cited by 365
Cited by10
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.gradeproof · cited by 7
- AddMonoidAlgebra.single_mem_gradeBystatement · cited by 4
- AddMonoidAlgebra.decomposeAuxstatement and proof · cited by 3
- AddMonoidAlgebra.decomposeAux_singlestatement and proof · cited by 3
- AddMonoidAlgebra.mem_gradeBy_iffstatement · cited by 1
- AddMonoidAlgebra.gradeBy_idstatement · cited by 0
- AddMonoidAlgebra.gradeBy.isInternalstatement and proof · cited by 0
- AddMonoidAlgebra.decomposeAux_coestatement and proof · cited by 0
- AddMonoidAlgebra.decomposeAux_eq_decomposestatement · cited by 0
- AddMonoidAlgebra.GradesBy.decompose_singlestatement · cited by 0