Theorems · Theorem · ring theory
QuaternionAlgebra.finrank_eq_four
∀ {R : Type u_3} (c₁ c₂ c₃ : R) [inst : CommRing R] [StrongRankCondition R],
Module.finrank R (QuaternionAlgebra R c₁ c₂ c₃) = 4- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingStrongRankCondition
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Cardinalproof · cited by 2,598
- Module.finrankstatement · cited by 1,770
- StrongRankConditionstatement and proof · cited by 286
- QuaternionAlgebrastatement and proof · cited by 174
- Cardinal.toNatproof · cited by 153
- QuaternionAlgebra.rank_eq_fourproof · cited by 2
- Cardinal.toNat_ofNatproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Quaternion.finrank_eq_fourproof · cited by 0