Theorems · Theorem · commutative algebra
Subalgebra.LinearDisjoint.include_range
∀ (R : Type u) [inst : CommSemiring R] (A : Type v) [inst_1 : Semiring A] (B : Type w) [inst_2 : Semiring B] [inst_3 : Algebra R A] [inst_4 : Algebra R B], Algebra.TensorProduct.includeLeft.range.LinearDisjoint Algebra.TensorProduct.includeRight.range
Images of two R-algebras A and B in A ⊗[R] B are linearly disjoint.
- Defined in
- Mathlib.RingTheory.LinearDisjoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapproof · cited by 10,215
- TensorProductstatement and proof · cited by 2,545
- LinearEquiv.symmproof · cited by 1,461
- AlgHom.rangestatement and proof · cited by 169
- Algebra.TensorProduct.includeRightstatement and proof · cited by 165
- LinearEquiv.injectiveproof · cited by 162
- Subalgebra.toSubmoduleproof · cited by 141
Cited by2
Results whose statement or proof uses this declaration.
- Subalgebra.LinearDisjoint.exists_field_of_isDomain_of_injectiveproof · cited by 2
- Algebra.TensorProduct.not_isField_of_transcendentalproof · cited by 1