Theorems · Definition · commutative algebra
Polynomial.degreeLT.basisProd
(R : Type u_1) →
[inst : Semiring R] →
(m n : ℕ) → Module.Basis (Fin (m + n)) R (↥(Polynomial.degreeLT R m) × ↥(Polynomial.degreeLT R n))Basis for R[X]_m × R[X]_n.
- Defined in
- Mathlib.RingTheory.Polynomial.DegreeLT
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 106 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.
Cites9
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
- Submodulestatement · cited by 7,192
- Polynomialstatement · cited by 5,681
- Module.Basisstatement · cited by 1,477
- Module.Basis.reindexproof · cited by 57
- Polynomial.degreeLTstatement · cited by 47
- finSumFinEquivproof · cited by 33
- Module.Basis.prodproof · cited by 26
- Polynomial.degreeLT.basisproof · cited by 15
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.degreeLT.addLinearEquivproof · cited by 12
- Polynomial.degreeLT.addLinearEquiv_castAddproof · cited by 1
- Polynomial.degreeLT.addLinearEquiv_natAddproof · cited by 1
- Polynomial.degreeLT.basisProd_castAddstatement · cited by 1
- Polynomial.degreeLT.basisProd_natAddstatement · cited by 1