Theorems · Theorem · field theory
IntermediateField.subsingleton_of_rank_adjoin_eq_one
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E],
(∀ (x : E), Module.rank F ↥F⟮x⟯ = 1) → Subsingleton (IntermediateField F E)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Cardinalstatement · cited by 2,598
- IntermediateFieldstatement · cited by 988
- Module.rankstatement and proof · cited by 496
- IntermediateField.adjoinstatement and proof · cited by 382
- subsingleton_of_bot_eq_topproof · cited by 8
- IntermediateField.bot_eq_top_of_rank_adjoin_eq_oneproof · cited by 1
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