Theorems · Definition · ring theory
QuadraticAlgebra.basis
{R : Type u_1} → (a b : R) → [inst : Semiring R] → Module.Basis (Fin 2) R (QuadraticAlgebra R a b)QuadraticAlgebra R a b has a basis over R given by 1 and i
- Defined in
- Mathlib.Algebra.QuadraticAlgebra.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- Semiringstatement and proof · cited by 13,802
- Module.Basisstatement · cited by 1,477
- QuadraticAlgebrastatement · cited by 123
- Module.Basis.ofEquivFunproof · cited by 7
- QuadraticAlgebra.linearEquivTupleproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- QuadraticAlgebra.rank_eq_twoproof · cited by 1
- QuadraticAlgebra.basis_repr_applystatement · cited by 0
- QuadraticAlgebra.det_toLinearMap_eq_normproof · cited by 0