Theorems · Theorem · ring theory
StarAlgHom.map_adjoin
∀ {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : Semiring B] [inst_6 : Algebra R B] [inst_7 : StarRing B]
[inst_8 : StarModule R A] [inst_9 : StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A),
StarSubalgebra.map f (StarAlgebra.adjoin R s) = StarAlgebra.adjoin R (⇑f '' s)- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Set.imagestatement · cited by 5,609
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- StarAlgHomstatement and proof · cited by 215
- StarSubalgebrastatement and proof · cited by 194
- StarAlgebra.adjoinstatement · cited by 42
- StarSubalgebra.mapstatement · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- range_cfcHom_leproof · cited by 2
- range_cfcHomproof · cited by 1