Theorems · Theorem · ring theory
AddMonoidAlgebra.of_apply
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddZeroClass M] (a : Multiplicative M),
(AddMonoidAlgebra.of R M) a = AddMonoidAlgebra.single (Multiplicative.toAdd a) 1- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Equivstatement · cited by 8,337
- MonoidHomstatement · cited by 3,629
- AddZeroClassstatement and proof · cited by 1,237
- Multiplicativestatement and proof · cited by 875
- AddMonoidAlgebrastatement · cited by 649
- AddMonoidAlgebra.singlestatement · cited by 250
- Multiplicative.toAddstatement · cited by 161
- AddMonoidAlgebra.ofstatement · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.freeAlgebra_lift_of_surjective_of_closureproof · cited by 0
- AddMonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closureproof · cited by 0