Theorems · Theorem · commutative algebra
PolynomialModule.single_add
∀ {R : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (n : ℕ) (m₁ m₂ : M),
PolynomialModule.single R n (m₁ + m₂) = PolynomialModule.single R n m₁ + PolynomialModule.single R n m₂- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Finsupp.singleproof · cited by 943
- Finsupp.extproof · cited by 399
- PolynomialModulestatement · cited by 76
- PolynomialModule.singlestatement · cited by 31
- Finsupp.single_addproof · cited by 23
- PolynomialModule.extproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.Filtration.submodule_eq_span_le_iff_stable_geproof · cited by 1