Theorems · Theorem · commutative algebra
Algebra.TensorProduct.includeLeft_injective
∀ {R : Type u_1} {S : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : Semiring A]
[inst_2 : Algebra R A] [inst_3 : Semiring B] [inst_4 : Algebra R B] [inst_5 : CommSemiring S] [inst_6 : Algebra S A]
[inst_7 : SMulCommClass R S A] [Module.Flat R A],
Function.Injective ⇑(algebraMap R B) → Function.Injective ⇑Algebra.TensorProduct.includeLeft- Defined in
- Mathlib.RingTheory.Flat.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomstatement · cited by 3,236
- TensorProductstatement and proof · cited by 2,545
- SMulCommClassstatement and proof · cited by 1,927
- LinearEquiv.symmproof · cited by 1,461
- TensorProduct.tmulproof · cited by 1,182
- map_oneproof · cited by 861
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.IsCentral.left_of_tensorproof · cited by 2
- Subalgebra.LinearDisjoint.exists_field_of_isDomain_of_injectiveproof · cited by 2
- PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparableproof · cited by 1
- Algebra.TensorProduct.not_isField_of_transcendentalproof · cited by 1
- CommRingCat.inl_injective_of_flatproof · cited by 0