Theorems · Definition · ring theory
QuaternionAlgebra.basisOneIJK
{R : Type u_3} → (c₁ c₂ c₃ : R) → [inst : CommRing R] → Module.Basis (Fin 4) R (QuaternionAlgebra R c₁ c₂ c₃)ℍ[R,c₁,c₂,c₃] has a basis over R given by 1, i, j, and k.
- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Module.Basisstatement · cited by 1,477
- QuaternionAlgebrastatement · cited by 174
- Module.Basis.ofEquivFunproof · cited by 7
- QuaternionAlgebra.linearEquivTupleproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- QuaternionAlgebra.rank_eq_fourproof · cited by 2
- QuaternionAlgebra.coe_basisOneIJK_reprstatement · cited by 0