Theorems · Theorem · field theory
IntermediateField.adjoin.powerBasis_gen
∀ {K : Type u} [inst : Field K] {L : Type u_3} [inst_1 : Field L] [inst_2 : Algebra K L] {x : L} (hx : IsIntegral K x),
(IntermediateField.adjoin.powerBasis hx).gen = IntermediateField.AdjoinSimple.gen K x- Cited by
- 10 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- IntermediateFieldstatement · cited by 988
- IsIntegralstatement and proof · cited by 427
- IntermediateField.adjoinstatement · cited by 382
- PowerBasis.genstatement and proof · cited by 122
- IntermediateField.AdjoinSimple.genstatement · cited by 55
- IntermediateField.adjoin.powerBasisstatement and proof · cited by 17
Cited by10
Results whose statement or proof uses this declaration.
- Algebra.norm_eq_prod_embeddingsproof · cited by 5
- X_pow_sub_C_irreducible_of_oddproof · cited by 3
- trace_eq_sum_embeddingsproof · cited by 3
- IntermediateField.card_algHom_adjoin_integralproof · cited by 2
- IntermediateField.AdjoinSimple.norm_gen_eq_prod_rootsproof · cited by 2
- IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_genproof · cited by 2
- trace_adjoinSimpleGenproof · cited by 2
- IntermediateField.AdjoinSimple.trace_gen_eq_sum_rootsproof · cited by 1
- PowerBasis.equivAdjoinSimple_symm_aevalproof · cited by 0
- PowerBasis.equivAdjoinSimple_symm_genproof · cited by 0