Theorems · Theorem · ring theory
MonoidAlgebra.mapRingHom_single
∀ {R : Type u_3} {S : Type u_4} {M : Type u_6} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : Monoid M]
(f : R →+* S) (a : M) (b : R),
(MonoidAlgebra.mapRingHom M f) (MonoidAlgebra.single a b) = MonoidAlgebra.single a (f b)- Defined in
- Mathlib.Algebra.MonoidAlgebra.MapDomain
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Monoidstatement and proof · cited by 3,887
- MonoidAlgebrastatement · cited by 590
- MonoidAlgebra.singlestatement and proof · cited by 253
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- MonoidAlgebra.mapRingHomstatement · cited by 27
- MonoidAlgebra.map_singleproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- MonoidAlgebra.mapRingHom_compproof · cited by 2
- MonoidAlgebra.lift_mapRingHom_algebraMapproof · cited by 1
- MonoidAlgebra.mapRingEquiv_singleproof · cited by 1
- MonoidAlgebra.mapRingHom_comp_algebraMapproof · cited by 1
- MonoidAlgebra.mapRingHom_comp_mapDomainRingHomproof · cited by 1
- MonoidAlgebra.mapRingHom_idproof · cited by 1
- MonoidAlgebra.mapRangeRingHom_singleproof · cited by 0
- MonoidAlgebra.lTensorAlgEquiv_symm_singleproof · cited by 0
- MonoidAlgebra.comulAlgHom_comp_mapRingHomproof · cited by 0
- MonoidAlgebra.scalarTensorEquiv_symm_singleproof · cited by 0
- MonoidAlgebra.counitAlgHom_comp_mapRingHomproof · cited by 0