Theorems · Theorem · commutative algebra
Submodule.span_range_natDegree_eq_adjoin
∀ {R : Type u_6} {A : Type u_7} [inst : CommRing R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {x : A}
{f : Polynomial R},
f.Monic →
(Polynomial.aeval x) f = 0 →
Submodule.span R ↑(Finset.image (fun x_1 => x ^ x_1) (Finset.range f.natDegree)) = Subalgebra.toSubmodule R[x]- Cited by
- 3 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites66
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
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Semiringstatement and proof · cited by 13,802
- Finsetstatement · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- Polynomialstatement and proof · cited by 5,681
- Set.imageproof · cited by 5,609
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
Cited by3
Results whose statement or proof uses this declaration.
- IsIntegral.fg_adjoin_singletonproof · cited by 13
- traceForm_dualSubmodule_adjoinproof · cited by 1
- span_coeff_minpolyDivproof · cited by 1