Theorems · Theorem · field theory
IntermediateField.finrank_eq_one_iff
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {K : IntermediateField F E},
Module.finrank F ↥K = 1 ↔ K = ⊥- Cited by
- 5 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Bot.botstatement and proof · cited by 4,720
- Module.finrankstatement and proof · cited by 1,770
- Subalgebraproof · cited by 1,353
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.toSubalgebraproof · cited by 134
- IntermediateField.toSubalgebra_injproof · cited by 6
- IntermediateField.bot_toSubalgebraproof · cited by 2
- Subalgebra.finrank_eq_one_iffproof · cited by 2
- IntermediateField.finrank_eq_finrank_subalgebraproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- IntermediateField.finrank_botproof · cited by 3
- NumberField.linearDisjoint_of_isGalois_isCoprime_discrproof · cited by 1
- IsGalois.of_card_aut_eq_finrankproof · cited by 1
- IntermediateField.finrank_adjoin_eq_one_iffproof · cited by 1
- isPurelyInseparable_of_finSepDegree_eq_oneproof · cited by 1