Theorems · Theorem · commutative algebra
Subalgebra.LinearDisjoint.symm
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S]
{A B : Subalgebra R S}, A.LinearDisjoint B → B.LinearDisjoint ALinear disjointness is symmetric in a commutative ring.
- Defined in
- Mathlib.RingTheory.LinearDisjoint
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- CommSemiringstatement and proof · cited by 10,911
- mul_commproof · cited by 2,262
- Subalgebrastatement and proof · cited by 1,353
- Subalgebra.LinearDisjointstatement and proof · cited by 75
- Subalgebra.LinearDisjoint.symm_of_commuteproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- IntermediateField.LinearDisjoint.symmproof · cited by 2
- Subalgebra.LinearDisjoint.basisOfBasisLeftproof · cited by 2
- Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_rightproof · cited by 1
- IntermediateField.LinearDisjoint.symm'proof · cited by 1
- Subalgebra.LinearDisjoint.basisOfBasisLeft_applyproof · cited by 1
- Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_applyproof · cited by 1
- Subalgebra.LinearDisjoint.of_linearDisjoint_finite_rightproof · cited by 1
- Subalgebra.linearDisjoint_commproof · cited by 0