Theorems · Definition · ring theory

AddMonoidAlgebra.mapRingEquiv

{R : Type u_3} →
  {S : Type u_4} →
    (M : Type u_6) →
      [inst : Semiring R] →
        [inst_1 : Semiring S] → [inst_2 : AddMonoid M] → R ≃+* S → AddMonoidAlgebra R M ≃+* AddMonoidAlgebra S M

Isomorphic rings have isomorphic additive monoid algebras.

Defined in: Mathlib.Algebra.MonoidAlgebra.MapDomain
Cited by: 5 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring Semiring AddMonoid

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Cites8

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
AddMonoidstatement and proof · cited by 2,864
RingEquivstatement and proof · cited by 1,147
RingHomClass.toRingHomproof · cited by 746
AddMonoidAlgebrastatement · cited by 649
RingEquiv.symmproof · cited by 567
AddMonoidAlgebra.mapRingHomproof · cited by 17
RingEquiv.ofRingHomproof · cited by 9

Cited by6

Results whose statement or proof uses this declaration.

MvPolynomial.mapEquivproof · cited by 8
AddMonoidAlgebra.mapRingEquiv_transstatement and proof · cited by 1
AddMonoidAlgebra.coeff_mapRingEquivstatement · cited by 1
AddMonoidAlgebra.symm_mapRingEquivstatement · cited by 0
AddMonoidAlgebra.mapRingEquiv_singlestatement · cited by 0
AddMonoidAlgebra.toRingHom_mapRingEquivstatement · cited by 0