Theorems · Definition · ring theory

AddMonoidAlgebra.mapDomainLinearEquiv

(R : Type u_1) →
  (S : Type u_2) →
    {M : Type u_3} →
      {N : Type u_4} →
        [inst : Semiring R] →
          [inst_1 : Semiring S] → [inst_2 : Module R S] → M ≃ N → AddMonoidAlgebra S M ≃ₗ[R] AddMonoidAlgebra S N

AddMonoidAlgebra.mapDomain as a linear equiv.

Defined in: Mathlib.Algebra.MonoidAlgebra.Module
Cited by: 4 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring Semiring Module

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

Cites10

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
RingHom.idstatement · cited by 18,349
Semiringstatement and proof · cited by 13,802
Equivstatement and proof · cited by 8,337
LinearEquivstatement · cited by 3,317
LinearEquiv.symmproof · cited by 1,461
AddMonoidAlgebrastatement · cited by 649
LinearEquiv.transproof · cited by 298
Finsupp.domLCongrproof · cited by 20
AddMonoidAlgebra.coeffLinearEquivproof · cited by 15

Cited by4

Results whose statement or proof uses this declaration.

AddMonoidAlgebra.mapDomainLinearEquiv_singlestatement · cited by 0
AddMonoidAlgebra.mapDomainLinearEquiv_transstatement · cited by 0
AddMonoidAlgebra.coeff_mapDomainLinearEquivstatement · cited by 0
AddMonoidAlgebra.symm_mapDomainLinearEquivstatement · cited by 0