Theorems · Definition · field theory
IntermediateField.AdjoinSimple.gen
(F : Type u_1) → [inst : Field F] → {E : Type u_2} → [inst_1 : Field E] → [inst_2 : Algebra F E] → (α : E) → ↥F⟮α⟯generator of F⟮α⟯
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- IntermediateField.adjoinstatement · cited by 382
- IntermediateField.mem_adjoin_simple_selfproof · cited by 19
Cited by58
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin.powerBasisproof · cited by 17
- IntermediateField.AdjoinSimple.algebraMap_genstatement · cited by 10
- IntermediateField.adjoin.powerBasis_genstatement · cited by 10
- IntermediateField.adjoinRootEquivAdjoinproof · cited by 5
- Algebra.norm_eq_prod_embeddingsproof · cited by 5
- Algebra.isIntegral_normproof · cited by 4
- IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_twoproof · cited by 4
- IntermediateField.minpoly_genstatement and proof · cited by 4
- isPowMul_spectralNormproof · cited by 3
- IntermediateField.AdjoinSimple.coe_aeval_gen_applystatement · cited by 3
- RatFunc.algEquivOfTranscendental_algebraMapstatement · cited by 3
- Algebra.FormallyEtale.of_isSeparableproof · cited by 3