Theorems · Theorem · ring theory
algebraMap_star_comm
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A] [inst_3 : StarMul A]
[inst_4 : Algebra R A] [StarModule R A] (r : R), (algebraMap R A) (star r) = star ((algebraMap R A) r)- Defined in
- Mathlib.Algebra.Star.Module
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- StarModulestatement and proof · cited by 570
- StarMulstatement and proof · cited by 195
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
- StarModule.star_smulproof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- inner_smul_left_eq_star_smulproof · cited by 4
- IsSelfAdjoint.algebraMapproof · cited by 2
- isSelfAdjoint_algebraMap_iffproof · cited by 0