Theorems · Theorem · commutative algebra
Module.FaithfullyFlat.injective_of_tensorProduct
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {T : Type u_3}
[inst_3 : CommRing T] [inst_4 : Algebra R T] [Module.FaithfullyFlat R S],
Function.Injective ⇑(algebraMap S (TensorProduct R S T)) → Function.Injective ⇑(algebraMap R T)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- TensorProductstatement and proof · cited by 2,545
- LinearMap.compproof · cited by 1,642
- one_smulproof · cited by 1,374
- TensorProduct.tmulproof · cited by 1,182
- LinearEquiv.toLinearMapproof · cited by 1,171
- map_oneproof · cited by 861
- LinearMap.extproof · cited by 844
Cited by2
Results whose statement or proof uses this declaration.
- RingHom.FaithfullyFlat.codescendsAlong_injectiveproof · cited by 1
- Module.FaithfullyFlat.bijective_of_tensorProductproof · cited by 0