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Theorems · Definition · ring theory

QuaternionAlgebra.Basis.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} → QuaternionAlgebra.Basis A c₁ c₂ c₃ → A

The second imaginary unit

Defined in
Mathlib.Algebra.QuaternionBasis
Cited by
23 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
CommRingRingAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

QuaternionAlgebra.Basis.i_mul_j · cited by 6Basis.i_mul_jQuaternionAlgebra.Basis.lift · cited by 6Basis.liftQuaternionAlgebra.Basis.compHom · cited by 4Basis.compHomQuaternionAlgebra.Basis.j_mul_i · cited by 4Basis.j_mul_iQuaternionAlgebra.Basis.j_mul_j · cited by 4Basis.j_mul_jQuaternionAlgebra.hom_ext · cited by 3QuaternionAlgebra.hom_extQuaternionAlgebra.Basis.ext · cited by 2Basis.extQuaternionAlgebra.Basis.i_mul_k · cited by 2Basis.i_mul_kQuaternionAlgebra.Basis.j_self · cited by 2Basis.j_selfQuaternionAlgebra.Basis.k_mul_j · cited by 2Basis.k_mul_jQuaternionAlgebra.Basis.j_mul_k · cited by 1Basis.j_mul_kQuaternionAlgebra.Basis.k_mul_i · cited by 1Basis.k_mul_iQuaternionAlgebra.Basis.k_mul_k · cited by 1Basis.k_mul_kQuaternion.hom_ext · cited by 1Quaternion.hom_extQuaternionAlgebra.Basis.ext_iff · cited by 0Basis.ext_iffCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRing · cited by 7463RingQuaternionAlgebra.Basis · cited by 28QuaternionAlgebra.BasisBasis.jCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by25

Results whose statement or proof uses this declaration.