Theorems · Theorem · commutative algebra
Module.Flat.tensorProduct_mapIncl_injective_of_right
∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_2} {N : Type u_3} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] (p : Submodule R M) (q : Submodule R N)
[Module.Flat R M] [Module.Flat R ↥q], Function.Injective ⇑(TensorProduct.mapIncl p q)If p and q are submodules of M and N respectively, and M and q are flat,
then p ⊗ q → M ⊗ N is injective.
- Defined in
- Mathlib.RingTheory.Flat.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement · cited by 2,545
- Submodule.subtypeproof · cited by 480
- Module.Flatstatement and proof · cited by 279
- Submodule.subtype_injectiveproof · cited by 25
- TensorProduct.mapInclstatement · cited by 14
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