Theorems · Theorem · field theory
IntermediateField.AdjoinSimple.algebraMap_gen
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (α : E),
(algebraMap (↥F⟮α⟯) E) (IntermediateField.AdjoinSimple.gen F α) = α- Cited by
- 10 results in Mathlib
- Foundations
- Depth 81 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- IntermediateField.AdjoinSimple.genstatement · cited by 55
Cited by10
Results whose statement or proof uses this declaration.
- IntermediateField.minpoly_genproof · cited by 4
- isPowMul_spectralNormproof · cited by 3
- trace_eq_trace_adjoinproof · cited by 3
- IntermediateField.AdjoinSimple.norm_gen_eq_prod_rootsproof · cited by 2
- IntermediateField.AdjoinSimple.isIntegral_genproof · cited by 1
- IntermediateField.aeval_gen_minpolyproof · cited by 1
- minpoly.exists_algEquiv_of_rootproof · cited by 1
- IntermediateField.AdjoinSimple.trace_gen_eq_sum_rootsproof · cited by 1
- spectralNorm_negproof · cited by 0
- spectralNorm_smulproof · cited by 0