Theorems · Theorem · commutative algebra
PowerBasis.dim_le_natDegree_of_root
∀ {S : Type u_2} [inst : Ring S] {A : Type u_4} [inst_1 : CommRing A] [inst_2 : Algebra A S] (pb : PowerBasis A S)
{p : Polynomial A}, p ≠ 0 → (Polynomial.aeval pb.gen) p = 0 → pb.dim ≤ p.natDegree- Defined in
- Mathlib.RingTheory.PowerBasis
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Semiringproof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Finset.univproof · cited by 3,473
- AlgHomstatement · cited by 3,236
- Finset.sum_congrproof · cited by 2,323
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.aevalstatement and proof · cited by 615
Cited by1
Results whose statement or proof uses this declaration.
- PowerBasis.dim_le_degree_of_rootproof · cited by 2