Theorems · Theorem · field theory
Field.primitive_element_iff_minpoly_degree_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).degree = ↑(Module.finrank F E)- Defined in
- Mathlib.FieldTheory.PrimitiveElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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
- WithBotstatement · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- IntermediateFieldstatement · cited by 988
- Polynomial.degreestatement · cited by 643
- minpolystatement and proof · cited by 439
- IntermediateField.adjoinstatement and proof · cited by 382
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