Theorems · Theorem · ring theory
NonUnitalStarAlgebra.adjoin_le_starAlgebra_adjoin
∀ (R : Type u_1) {A : Type u_2} [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 : Set A),
NonUnitalStarAlgebra.adjoin R s ≤ (StarAlgebra.adjoin R s).toNonUnitalStarSubalgebra- 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- NonUnitalStarSubalgebrastatement · cited by 196
- NonUnitalStarAlgebra.adjoinstatement · cited by 43
- StarAlgebra.adjoinstatement · cited by 42
- StarSubalgebra.toNonUnitalStarSubalgebrastatement · cited by 10
- StarAlgebra.subset_adjoinproof · cited by 10
- NonUnitalStarAlgebra.adjoin_leproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- StarAlgebra.adjoin_nonUnitalStarSubalgebraproof · cited by 2
- ContinuousMap.ker_evalStarAlgHom_inter_adjoin_idproof · cited by 1