Theorems · Theorem · field theory
minpoly.natDegree_le
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : Ring B] [inst_2 : Algebra A B] [Module.Finite A B] (x : B)
[Module.Free A B], (minpoly A x).natDegree ≤ Module.finrank A B- Defined in
- Mathlib.FieldTheory.Minpoly.Finite
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Nontrivialproof · cited by 2,416
- Module.finrankstatement · cited by 1,770
- Polynomial.natDegreestatement and proof · cited by 1,105
- Module.Finitestatement and proof · cited by 1,032
- Module.Freestatement and proof · cited by 597
- minpolystatement and proof · cited by 439
- Polynomial.natDegree_of_subsingletonproof · cited by 21
- Module.finrank_subsingletonproof · cited by 11
- Module.finrank_eq_spanFinrank_of_freeproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.Embeddings.finite_of_norm_leproof · cited by 4
- NumberField.Embeddings.coeff_bdd_of_norm_leproof · cited by 3
- Irreducible.natDegree_le_twoproof · cited by 2
- sum_smul_minpolyDiv_eq_X_powproof · cited by 1
- Valuation.pow_coeff_zero_ne_zero_of_unitproof · cited by 0
- minpoly.degree_leproof · cited by 0