Theorems · Definition · ring theory
AddMonoidAlgebra.coeff
{R : Type u_8} → {M : Type u_9} → [inst : Semiring R] → AddMonoidAlgebra R M → M →₀ RThe coefficients M →₀ R of an element of the additive monoid algebra R[M].
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 365 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 88 definitions · uses no axioms
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Finsuppstatement · cited by 5,255
- AddMonoidAlgebrastatement and proof · cited by 649
Cited by396
Results whose statement or proof uses this declaration.
- Polynomial.coeffproof · cited by 1,045
- MvPolynomial.coeffproof · cited by 315
- Polynomial.supportproof · cited by 237
- MvPolynomial.supportproof · cited by 220
- MvPolynomial.eval₂proof · cited by 103
- AddMonoidAlgebra.extstatement · cited by 90
- Algebra.Generators.compproof · cited by 52
- Polynomial.coeff_subproof · cited by 49
- AddMonoidAlgebra.supDegreeproof · cited by 49
- MvPolynomial.induction_onproof · cited by 43
- Polynomial.coeff_monomialproof · cited by 40
- MvPolynomial.mem_support_iffproof · cited by 37
Showing the 200 most cited of 396.