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Theorems · Definition · ring theory

AddMonoidAlgebra.uniqueLinearEquiv

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

The trivial monoid algebra is the base ring.

Defined in
Mathlib.Algebra.MonoidAlgebra.Module
Cited by
2 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringSemiringModuleZeroSubsingleton
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddMonoidAlgebra.uniqueLinearEquiv_apply · cited by 0AddMonoidAlgebra.uniqueLi…AddMonoidAlgebra.uniqueLinearEquiv_symm_apply · cited by 0AddMonoidAlgebra.uniqueLi…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearEquiv · cited by 3317LinearEquivAddEquiv · cited by 1087AddEquivAddMonoidAlgebra · cited by 649AddMonoidAlgebraEquiv.toFun · cited by 279Equiv.toFunAddEquiv.toEquiv · cited by 174AddEquiv.toEquivEquiv.invFun · cited by 163Equiv.invFunAddEquiv.trans · cited by 53AddEquiv.transAddMonoidAlgebra.coeffAddEquiv · cited by 12AddMonoidAlgebra.coeffAdd…Finsupp.uniqueAddEquiv · cited by 5Finsupp.uniqueAddEquivAddMonoidAlgebra.uniqueLinear…CITED BYCITES

Cites12

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Cited by2

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