Theorems · Theorem · field theory
IntermediateField.finrank_eq_one_iff_eq_top
∀ {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 (↥K) E = 1 ↔ K = ⊤- Cited by
- 3 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Bot.botproof · cited by 4,720
- Module.finrankstatement · cited by 1,770
- IntermediateFieldstatement and proof · cited by 988
- AlgHom.toRingHomproof · cited by 490
- top_le_iffproof · cited by 175
- Algebra.ofIdproof · cited by 166
- IntermediateField.mem_topproof · cited by 7
- Subalgebra.bot_eq_top_iff_finrank_eq_oneproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.trace_eq_zero_of_not_isSeparableproof · cited by 2
- IntermediateField.bot_eq_top_iff_finrank_eq_oneproof · cited by 1
- isSeparable_iff_finInsepDegree_eq_oneproof · cited by 0