Theorems · Definition · ring theory
FreeAlgebra.basisFreeMonoid
(R : Type u) → (X : Type v) → [inst : CommSemiring R] → Module.Basis (FreeMonoid X) R (FreeAlgebra R X)
The FreeMonoid X basis on the FreeAlgebra R X,
mapping [x₁, x₂, ..., xₙ] to the "monomial" 1 • x₁ * x₂ * ⋯ * xₙ
- Defined in
- Mathlib.LinearAlgebra.FreeAlgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Module.Basisstatement · cited by 1,477
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.transproof · cited by 298
- FreeMonoidstatement · cited by 147
- AlgEquiv.toLinearEquivproof · cited by 117
- Module.Basis.mapproof · cited by 70
- FreeAlgebrastatement · cited by 48
- MonoidAlgebra.coeffLinearEquivproof · cited by 34
- Finsupp.basisSingleOneproof · cited by 16
- FreeAlgebra.equivMonoidAlgebraFreeMonoidproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- FreeAlgebra.rank_eqproof · cited by 2
- Module.Basis.tensorAlgebraproof · cited by 1
- Module.Basis.tensorAlgebra_repr_applystatement · cited by 0