Theorems · Theorem · ring theory
MonoidAlgebra.of_apply
∀ (R : Type u_8) (M : Type u_9) [inst : Semiring R] [inst_1 : MulOneClass M] (a : M), (MonoidAlgebra.of R M) a = MonoidAlgebra.single a 1
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MonoidHomstatement · cited by 3,629
- MulOneClassstatement and proof · cited by 1,018
- MonoidAlgebrastatement · cited by 590
- MonoidAlgebra.singlestatement · cited by 253
- MonoidAlgebra.ofstatement and proof · cited by 30
Cited by26
Results whose statement or proof uses this declaration.
- MonoidAlgebra.induction_onproof · cited by 6
- MonoidAlgebra.ringHom_ext'proof · cited by 3
- Representation.asModuleEquiv_symm_map_rhoproof · cited by 2
- MonoidAlgebra.lift_ofproof · cited by 1
- Representation.ofModule_asAlgebraHom_apply_applyproof · cited by 1
- Representation.ofModule_asModule_actproof · cited by 1
- MonoidAlgebra.rTensorEquivAlgEquiv.invFun_tmulproof · cited by 1
- FDRep.average_char_eq_finrank_invariantsproof · cited by 1
- Representation.asAlgebraHom_ofMulAction_smul_eq_mulproof · cited by 1
- GroupAlgebra.mul_average_leftproof · cited by 1
- Representation.averageMap_idproof · cited by 1
- Representation.card_inv_mul_sum_char_eq_finrankproof · cited by 1