Theorems · Theorem · commutative algebra
Subalgebra.LinearDisjoint.of_le_right_of_flat
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] {A B : Subalgebra R S},
A.LinearDisjoint B → ∀ {B' : Subalgebra R S}, B' ≤ B → ∀ [Module.Flat R ↥A], A.LinearDisjoint B'- Defined in
- Mathlib.RingTheory.LinearDisjoint
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Subalgebrastatement and proof · cited by 1,353
- Module.Flatstatement and proof · cited by 279
- Subalgebra.LinearDisjointstatement and proof · cited by 75
- Submodule.LinearDisjoint.of_le_right_of_flatproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- IntermediateField.LinearDisjoint.of_le_right'proof · cited by 1
- IntermediateField.LinearDisjoint.of_le_rightproof · cited by 1
- Subalgebra.LinearDisjoint.of_le_of_flat_leftproof · cited by 0
- Subalgebra.LinearDisjoint.of_le_of_flat_rightproof · cited by 0