Theorems · Theorem · nonassociative algebras
NonUnitalAlgebra.adjoin_le_centralizer_centralizer
∀ (R : Type u_1) {A : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : Module R A]
[inst_3 : IsScalarTower R A A] [inst_4 : SMulCommClass R A A] (s : Set A),
NonUnitalAlgebra.adjoin R s ≤ NonUnitalSubalgebra.centralizer R ↑(NonUnitalSubalgebra.centralizer R s)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 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
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalSubalgebrastatement · cited by 215
- NonUnitalAlgebra.adjoinstatement · cited by 33
- Set.subset_centralizer_centralizerproof · cited by 13
- NonUnitalSubalgebra.centralizerstatement · cited by 12
- NonUnitalAlgebra.adjoin_leproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.adjoin_le_centralizer_centralizerproof · cited by 2
- NonUnitalAlgebra.commute_of_mem_adjoin_of_forall_mem_commuteproof · cited by 2
- NonUnitalSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizerproof · cited by 1
- NonUnitalAlgebra.isMulCommutative_adjoinproof · cited by 0