Theorems · Theorem · field theory
IntermediateField.LinearDisjoint.rank_sup
∀ {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 → Module.rank F ↥(A ⊔ B) = Module.rank F ↥A * Module.rank F ↥BIf A and B are linearly disjoint over F, then the
rank of A ⊔ B is equal to the product of that of A and B.
- Defined in
- Mathlib.FieldTheory.LinearDisjoint
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- LE.le.transproof · cited by 3,151
- Cardinalstatement · cited by 2,598
- IntermediateFieldstatement and proof · cited by 988
- LE.le.antisymmproof · cited by 507
- Module.rankstatement · cited by 496
- Eq.geproof · cited by 375
- AlgHom.toLinearMapproof · cited by 254
- IntermediateField.toSubalgebraproof · cited by 134
- IntermediateField.LinearDisjointstatement and proof · cited by 82
- Subalgebra.inclusionproof · cited by 36
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.LinearDisjoint.finrank_supproof · cited by 1