Theorems · Theorem · ring theory
StarSubalgebra.algebraMap_mem
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : StarRing A] [inst_4 : Algebra R A] [inst_5 : StarModule R A] (S : StarSubalgebra R A) (r : R),
(algebraMap R A) r ∈ S- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement and proof · cited by 194
- StarSubalgebra.toSubalgebraproof · cited by 58
- Subalgebra.algebraMap_mem'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- StarSubalgebra.smul_memproof · cited by 2
- StarSubalgebra.range_subsetproof · cited by 1
- StarSubalgebra.rangeS_leproof · cited by 0