Theorems · Definition · commutative algebra
PolynomialModule.coeffEquiv
(R : Type u_2) →
{M : Type u_3} →
[inst : CommRing R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → PolynomialModule R M ≃ (ℕ →₀ M)PolynomialModule.coeff as an equiv.
- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddCommGroupstatement and proof · cited by 12,871
- Equivstatement · cited by 8,337
- Finsuppstatement · cited by 5,255
- PolynomialModulestatement · cited by 76
- PolynomialModule.coeffproof · cited by 27
Cited by8
Results whose statement or proof uses this declaration.
- PolynomialModule.coeffAddEquivproof · cited by 6
- PolynomialModule.coeffLinearEquivproof · cited by 5
- PolynomialModule.coeff_injectiveproof · cited by 1
- PolynomialModule.ofCoeff_injectiveproof · cited by 1
- PolynomialModule.coeffEquiv_applystatement and proof · cited by 0
- PolynomialModule.coeffEquiv_symm_applystatement and proof · cited by 0
- PolynomialModule.existsproof · cited by 0
- PolynomialModule.forallproof · cited by 0