Mathlib Map

Theorems · Definition · ring theory

AddMonoidAlgebra.mapAddEquiv

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

Additively isomorphic rings have additively isomorphic additive monoid algebras. AddMonoidAlgebra.map as an AddEquiv.

Defined in
Mathlib.Algebra.MonoidAlgebra.MapDomain
Cited by
9 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringSemiringAdd
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddMonoidAlgebra.opRingEquiv · cited by 6AddMonoidAlgebra.opRingEq…AddMonoidAlgebra.mapAddEquiv_single · cited by 3AddMonoidAlgebra.mapAddEq…AddMonoidAlgebra.opRingEquiv_apply · cited by 3AddMonoidAlgebra.opRingEq…Polynomial.opRingEquiv_op_monomial · cited by 3Polynomial.opRingEquiv_op…Polynomial.coeff_opRingEquiv · cited by 2Polynomial.coeff_opRingEq…AddMonoidAlgebra.coeff_mapAddEquiv · cited by 2AddMonoidAlgebra.coeff_ma…AddMonoidAlgebra.opRingEquiv_symm_apply · cited by 1AddMonoidAlgebra.opRingEq…AddMonoidAlgebra.mapAddEquiv_trans · cited by 0AddMonoidAlgebra.mapAddEq…AddMonoidAlgebra.opRingEquiv_single · cited by 0AddMonoidAlgebra.opRingEq…AddMonoidAlgebra.symm_mapAddEquiv · cited by 0AddMonoidAlgebra.symm_map…Semiring · cited by 13802SemiringAddEquiv · cited by 1087AddEquivAddMonoidAlgebra · cited by 649AddMonoidAlgebraAddEquiv.symm · cited by 530AddEquiv.symmAddMonoidHomClass.toAddMonoidHom · cited by 232AddMonoidHomClass.toAddMo…AddMonoidAlgebra.map · cited by 21AddMonoidAlgebra.mapAddMonoidAlgebra.mapAddEquivCITED BYCITES

Cites6

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Cited by10

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