Theorems · Theorem · field theory
IntermediateField.minpoly_gen
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (α : E),
minpoly F (IntermediateField.AdjoinSimple.gen F α) = minpoly F α- Cited by
- 4 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IntermediateFieldstatement · cited by 988
- minpolystatement and proof · cited by 439
- IntermediateField.adjoinstatement and proof · cited by 382
- RingHom.injectiveproof · cited by 187
- IntermediateField.AdjoinSimple.genstatement and proof · cited by 55
- IntermediateField.AdjoinSimple.algebraMap_genproof · cited by 10
- minpoly.algebraMap_eqproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- X_pow_sub_C_irreducible_of_oddproof · cited by 3
- trace_adjoinSimpleGenproof · cited by 2
- IntermediateField.card_algHom_adjoin_integralproof · cited by 2
- IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_genproof · cited by 2