Theorems · Theorem · ring theory
IsSelfAdjoint.algebraMap
∀ {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}, IsSelfAdjoint r → IsSelfAdjoint ((algebraMap R A) r)- Defined in
- Mathlib.Algebra.Star.Module
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- IsSelfAdjointstatement and proof · cited by 545
- StarMulstatement and proof · cited by 195
- IsSelfAdjoint.star_eqproof · cited by 58
- algebraMap_star_commproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- SpectrumRestricts.nnreal_iff_nnnormproof · cited by 2
- isSelfAdjoint_algebraMap_iffproof · cited by 0