Theorems · Theorem · ring theory
DirectSum.toSemiring_coe_addMonoidHom
∀ {ι : Type u_1} [inst : DecidableEq ι] {A : ι → Type u_2} {R : Type u_3} [inst_1 : (i : ι) → AddCommMonoid (A i)]
[inst_2 : AddMonoid ι] [inst_3 : DirectSum.GSemiring A] [inst_4 : Semiring R] (f : (i : ι) → A i →+ R)
(hone : (f 0) GradedMonoid.GOne.one = 1)
(hmul : ∀ {i j : ι} (ai : A i) (aj : A j), (f (i + j)) (GradedMonoid.GMul.mul ai aj) = (f i) ai * (f j) aj),
↑(DirectSum.toSemiring f hone hmul) = DirectSum.toAddMonoid f- Defined in
- Mathlib.Algebra.DirectSum.Ring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- RingHomstatement · cited by 10,189
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- DirectSumstatement · cited by 446
- AddMonoidHomClass.toAddMonoidHomstatement · cited by 232
- GradedMonoid.GMul.mulstatement and proof · cited by 45
- DirectSum.GSemiringstatement and proof · cited by 39
- GradedMonoid.GOne.onestatement and proof · cited by 32
- DirectSum.toAddMonoidstatement · cited by 11
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