Theorems · Definition · commutative algebra
PolynomialModule.coeff
{R : Type u_1} →
{M : Type u_2} →
[inst : CommRing R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → PolynomialModule R M → ℕ →₀ MThe coefficients ℕ →₀ M of an element of the additive monoid algebra M[X].
- Defined in
- Mathlib.Algebra.Polynomial.Module.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Finsuppstatement · cited by 5,255
- PolynomialModulestatement and proof · cited by 76
Cited by30
Results whose statement or proof uses this declaration.
- PolynomialModule.evalproof · cited by 17
- Ideal.Filtration.submoduleproof · cited by 7
- PolynomialModule.induction_linearproof · cited by 6
- PolynomialModule.coeffEquivproof · cited by 6
- PolynomialModule.extstatement · cited by 4
- PolynomialModule.coeff_singlestatement · cited by 3
- PolynomialModule.coeff_injstatement · cited by 2
- PolynomialModule.coeff_finsuppSumstatement · cited by 1
- PolynomialModule.coeff_injectivestatement · cited by 1
- PolynomialModule.smul_single_applystatement and proof · cited by 1
- Ideal.Filtration.submodule_closure_singleproof · cited by 1
- Ideal.Filtration.submodule_eq_span_le_iff_stable_geproof · cited by 1