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Theorems · Definition · ring theory

AddMonoidAlgebra.coeffLinearEquiv

(R : Type u_1) →
  {S : Type u_2} →
    {M : Type u_3} →
      [inst : Semiring R] → [inst_1 : Semiring S] → [inst_2 : Module R S] → AddMonoidAlgebra S M ≃ₗ[R] M →₀ S

MonoidAlgebra.coeff as a linear equiv.

Defined in
Mathlib.Algebra.MonoidAlgebra.Module
Cited by
15 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringSemiringModule

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPolynomial.weightedHomogeneousComponent · cited by 25MvPolynomial.weightedHomo…AddMonoidAlgebra.lsingle · cited by 14AddMonoidAlgebra.lsingleAddMonoidAlgebra.supported · cited by 12AddMonoidAlgebra.supportedAddMonoidAlgebra.coeffLinearEquiv_apply · cited by 11AddMonoidAlgebra.coeffLin…Algebra.Generators.H1Cotangent.δAux · cited by 10H1Cotangent.δAuxMvPolynomial.coeff_weightedHomogeneousComponent · cited by 8MvPolynomial.coeff_weight…AddMonoidAlgebra.coeffLinearEquiv_symm_apply · cited by 7AddMonoidAlgebra.coeffLin…MvPolynomial.basisMonomials · cited by 6MvPolynomial.basisMonomia…AddMonoidAlgebra.supported_eq_span_single · cited by 5AddMonoidAlgebra.supporte…AddMonoidAlgebra.tensorEquiv · cited by 4AddMonoidAlgebra.tensorEq…AddMonoidAlgebra.comul_single · cited by 4AddMonoidAlgebra.comul_si…AddMonoidAlgebra.mapDomainLinearEquiv · cited by 4AddMonoidAlgebra.mapDomai…AddMonoidAlgebra.mapDomainLinearMap · cited by 3AddMonoidAlgebra.mapDomai…MvPolynomial.mkDerivationₗ · cited by 3MvPolynomial.mkDerivationₗMvPolynomial.weightedHomogeneousComponent_apply · cited by 3MvPolynomial.weightedHomo…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringFinsupp · cited by 5255FinsuppLinearEquiv · cited by 3317LinearEquivAddMonoidAlgebra · cited by 649AddMonoidAlgebraAddMonoidAlgebra.coeffEquiv · cited by 22AddMonoidAlgebra.coeffEqu…Equiv.linearEquiv · cited by 9Equiv.linearEquivAddMonoidAlgebra.coeffLinearE…CITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by26

Results whose statement or proof uses this declaration.