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Theorems · Theorem · ring theory

QuaternionAlgebra.Basis.k_mul_j

∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {c₁ c₂ c₃ : R}
  (q : QuaternionAlgebra.Basis A c₁ c₂ c₃), q.k * q.j = c₃ • q.i
Defined in
Mathlib.Algebra.QuaternionBasis
Cited by
2 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
CommRingRingAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

QuaternionAlgebra.Basis.j_mul_k · cited by 1Basis.j_mul_kQuaternionAlgebra.Basis.lift_mul · cited by 0Basis.lift_mulCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRing · cited by 7463Ringmul_one · cited by 3885mul_onemul_assoc · cited by 1667mul_assocmul_smul_comm · cited by 65mul_smul_commQuaternionAlgebra.Basis · cited by 28QuaternionAlgebra.BasisQuaternionAlgebra.Basis.i · cited by 23Basis.iQuaternionAlgebra.Basis.j · cited by 23Basis.jQuaternionAlgebra.Basis.k · cited by 16Basis.kQuaternionAlgebra.Basis.i_mul_j · cited by 6Basis.i_mul_jQuaternionAlgebra.Basis.j_mul_j · cited by 4Basis.j_mul_jBasis.k_mul_jCITED BYCITES

Cites12

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Cited by2

Results whose statement or proof uses this declaration.