Theorems · Theorem · field theory
IntermediateField.mem_adjoin_simple_self
∀ (F : Type u_1) [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (α : E), α ∈ F⟮α⟯- Cited by
- 19 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.mem_singletonproof · cited by 183
- IntermediateField.subset_adjoinproof · cited by 59
Cited by20
Results whose statement or proof uses this declaration.
- IntermediateField.AdjoinSimple.genproof · cited by 55
- IntermediateField.isSeparable_adjoin_simple_iff_isSeparableproof · cited by 4
- IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparableproof · cited by 4
- IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_twoproof · cited by 4
- IntermediateField.AdjoinSimple.coe_aeval_gen_applyproof · cited by 3
- IntermediateField.exists_lt_finrank_of_infinite_dimensionalproof · cited by 3
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
- Field.primitive_element_inf_auxproof · cited by 1
- isPurelyInseparable_of_finSepDegree_eq_oneproof · cited by 1
- IntermediateField.exists_finset_of_mem_supr'proof · cited by 1
- exists_root_adjoin_eq_top_of_isCyclicproof · cited by 1
- Field.isAlgebraic_of_adjoin_eq_adjoinproof · cited by 1