Theorems · Definition · ring theory
AddMonoidAlgebra.coeffEquiv
{R : Type u_1} → {M : Type u_4} → [inst : Semiring R] → AddMonoidAlgebra R M ≃ (M →₀ R)AddMonoidAlgebra.coeff as an equiv.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- Semiring
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.
- Semiringstatement and proof · cited by 13,802
- Equivstatement · cited by 8,337
- Finsuppstatement · cited by 5,255
- AddMonoidAlgebrastatement · cited by 649
- AddMonoidAlgebra.coeffproof · cited by 365
Cited by24
Results whose statement or proof uses this declaration.
- Polynomial.coeff_addproof · cited by 77
- AddMonoidAlgebra.coeffLinearEquivproof · cited by 15
- MvPolynomial.coeff_subproof · cited by 14
- AddMonoidAlgebra.coeffAddEquivproof · cited by 12
- IsAlgebraic.restrictScalarsproof · cited by 6
- AddMonoidAlgebra.cardinalMk_eq_max_lift_of_infiniteproof · cited by 4
- AddMonoidAlgebra.coeffEquiv_applystatement and proof · cited by 4
- AddMonoidAlgebra.coeffEquiv_symm_applystatement and proof · cited by 4
- Polynomial.sum_add_indexproof · cited by 3
- AddMonoidAlgebra.coeff_injectiveproof · cited by 3
- MvPolynomial.coeff_negproof · cited by 2
- AddMonoidAlgebra.cardinalMk_eq_lift_of_fintypeproof · cited by 2