Theorems · Definition · commutative algebra
MvPolynomial.basisMonomials
(σ : Type u) → (R : Type v) → [inst : CommSemiring R] → Module.Basis (σ →₀ ℕ) R (MvPolynomial σ R)
The monomials form a basis on MvPolynomial σ R.
- Defined in
- Mathlib.RingTheory.MvPolynomial.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 80 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.
Cites5
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
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- Module.Basisstatement · cited by 1,477
- AddMonoidAlgebra.coeffLinearEquivproof · cited by 15
Cited by7
Results whose statement or proof uses this declaration.
- MvPolynomial.rank_eq_liftproof · cited by 3
- Module.Basis.symmetricAlgebraproof · cited by 1
- MvPolynomial.linearIndependent_Xproof · cited by 1
- MvPolynomial.rank_eqproof · cited by 0
- Module.Basis.symmetricAlgebra_repr_applystatement · cited by 0
- MvPolynomial.finrank_eq_zeroproof · cited by 0
- MvPolynomial.coe_basisMonomialsstatement · cited by 0