Theorems · Theorem · ring theory
AddMonoidAlgebra.gradeBy.isInternal
∀ {M : Type u_1} {ι : Type u_2} {R : Type u_3} [inst : AddMonoid M] [inst_1 : DecidableEq ι] [inst_2 : AddMonoid ι]
[inst_3 : CommSemiring R] (f : M →+ ι), DirectSum.IsInternal (AddMonoidAlgebra.gradeBy R ⇑f)AddMonoidAlgebra.gradeBy describe an internally graded algebra.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Grading
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement · cited by 7,192
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- AddMonoidAlgebrastatement · cited by 649
- DirectSum.IsInternalstatement · cited by 65
- AddMonoidAlgebra.gradeBystatement and proof · cited by 8
- DirectSum.Decomposition.isInternalproof · cited by 6
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.