Theorems · Theorem · commutative algebra
PolynomialModule.coeff_sum
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
(s : Finset ι) (f : ι → PolynomialModule R M), (∑ i ∈ s, f i).coeff = ∑ i ∈ s, (f i).coeff- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Finsuppstatement · cited by 5,255
- Finset.sumstatement · cited by 5,195
- map_sumproof · cited by 455
- PolynomialModulestatement and proof · cited by 76
- PolynomialModule.coeffstatement · cited by 27
- PolynomialModule.coeffAddEquivproof · cited by 6
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