Theorems · Theorem · ring theory
AddMonoidAlgebra.liftNC_smul
∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddZeroClass M]
(f : S →+* R) (g : Multiplicative M →* R) (c : S) (φ : AddMonoidAlgebra S M),
(AddMonoidAlgebra.liftNC ↑f ⇑g) (c • φ) = f c * (AddMonoidAlgebra.liftNC ↑f ⇑g) φ- Defined in
- Mathlib.Algebra.MonoidAlgebra.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringSemiringAddZeroClass
Around this declaration
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Cites22
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
- MonoidHomstatement and proof · cited by 3,629
- AddMonoidHomstatement · cited by 3,230
- mul_assocproof · cited by 1,667
- AddZeroClassstatement and proof · cited by 1,237
- map_mulproof · cited by 1,137
- Multiplicativestatement and proof · cited by 875
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidHom.compproof · cited by 339
- DFunLike.congr_funproof · cited by 288
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