Theorems · Theorem · field theory
IntermediateField.LinearDisjoint.inf_eq_bot
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {A B : IntermediateField F E},
A.LinearDisjoint ↥B → A ⊓ B = ⊥If A and B are linearly disjoint over F, then their intersection is equal to F.
This is actually an equivalence if A/F and B/F are finite dimensional, and A/F is Galois,
see IntermediateField.LinearDisjoint.iff_inf_eq_bot.
- Defined in
- Mathlib.FieldTheory.LinearDisjoint
- Cited by
- 2 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.
Cites8
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
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.LinearDisjointstatement and proof · cited by 82
- IntermediateField.linearDisjoint_iff'proof · cited by 19
- IntermediateField.toSubalgebra_injectiveproof · cited by 11
- Subalgebra.LinearDisjoint.inf_eq_botproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.LinearDisjoint.iff_inf_eq_botproof · cited by 0
- IntermediateField.LinearDisjoint.eq_bot_of_selfproof · cited by 0