Theorems · Definition · ring theory
AddMonoidAlgebra.grade
{M : Type u_1} → (R : Type u_3) → [inst : CommSemiring R] → M → Submodule R (AddMonoidAlgebra R M)The submodule corresponding to each grade.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Grading
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 81 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.
Cites4
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
- AddMonoidAlgebrastatement · cited by 649
- AddMonoidAlgebra.gradeByproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.single_mem_gradestatement · cited by 1
- AddMonoidAlgebra.mem_grade_iffstatement and proof · cited by 1
- AddMonoidAlgebra.mem_grade_iff'statement · cited by 1
- AddMonoidAlgebra.gradeBy_idstatement · cited by 0
- AddMonoidAlgebra.grade_eq_lsingle_rangestatement · cited by 0
- AddMonoidAlgebra.grade.decompose_singlestatement · cited by 0
- AddMonoidAlgebra.grade.isInternalstatement and proof · cited by 0