Theorems · Theorem · ring theory
QuaternionAlgebra.rank_eq_four
∀ {R : Type u_3} (c₁ c₂ c₃ : R) [inst : CommRing R] [StrongRankCondition R],
Module.rank R (QuaternionAlgebra R c₁ c₂ c₃) = 4- Defined in
- Mathlib.Algebra.Quaternion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 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.
Cites8
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
- Cardinalstatement and proof · cited by 2,598
- Module.rankstatement · cited by 496
- StrongRankConditionstatement and proof · cited by 286
- Fintype.card_finproof · cited by 270
- QuaternionAlgebrastatement · cited by 174
- rank_eq_card_basisproof · cited by 8
- QuaternionAlgebra.basisOneIJKproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- QuaternionAlgebra.finrank_eq_fourproof · cited by 1
- Quaternion.rank_eq_fourproof · cited by 0