Theorems · Theorem · field theory
Field.primitive_element_iff_minpoly_natDegree_eq
∀ (F : Type u_3) {E : Type u_4} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [FiniteDimensional F E]
(α : E), F⟮α⟯ = ⊤ ↔ (minpoly F α).natDegree = Module.finrank F E- Defined in
- Mathlib.FieldTheory.PrimitiveElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- Polynomial.natDegreestatement · cited by 1,105
- IntermediateFieldstatement and proof · cited by 988
- minpolystatement · cited by 439
- le_topproof · cited by 411
- IntermediateField.adjoinstatement and proof · cited by 382
- finrank_topproof · cited by 31
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.hermiteTheorem.natDegree_le_rankOfDiscrBddproof · cited by 2
- Field.primitive_element_iff_minpoly_degree_eqproof · cited by 0