Theorems · Theorem · ring theory
Algebra.algebraMap_eq_smul_one
∀ {R : Type u} {A : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (r : R),
(algebraMap R A) r = r • 1- Defined in
- Mathlib.Algebra.Algebra.Defs
- Cited by
- 119 results in Mathlib
- Foundations
- Depth 18 from the axioms, rests on 139 definitions · uses no axioms
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_oneproof · cited by 3,885
- Algebra.smul_defproof · cited by 287
Cited by119
Results whose statement or proof uses this declaration.
- IsScalarTower.algebraMap_eqproof · cited by 110
- algebraMap_memproof · cited by 23
- IsScalarTower.algebraMap_smulproof · cited by 19
- algebraMap_applyproof · cited by 7
- smul_algebraMapproof · cited by 7
- spectrum.zero_eqproof · cited by 7
- Algebra.Extension.CotangentSpace.map_tmulproof · cited by 7
- spectrum.algebraMap_mem_iffproof · cited by 6
- Algebra.TensorProduct.tmul_one_eq_one_tmulproof · cited by 5
- Polynomial.aeval_algebraMap_eq_zero_iffproof · cited by 5
- norm_algebraMapproof · cited by 5
- CliffordAlgebra.changeForm_algebraMapproof · cited by 4