Theorems · Theorem · commutative algebra
Module.Flat.toAlgebra_injective
∀ {R : Type u} {M : Type v} {A : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Semiring A] [inst_4 : Algebra R A] (e : TensorProduct R A M ≃ₗ[A] A) [Module.Flat R M] [FaithfulSMul R A],
Function.Injective ⇑(Module.Flat.toAlgebra e)- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- LinearEquivstatement and proof · cited by 3,317
- TensorProductstatement and proof · cited by 2,545
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
Cited by1
Results whose statement or proof uses this declaration.
- Module.Flat.submoduleAlgebraEquivproof · cited by 2