Theorems · Theorem · commutative algebra

Submodule.baseChange_inj

∀ {R : Type u_1} {M : Type u_2} {A : Type u_3} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A]
  [Module.FaithfullyFlat R A] [inst_4 : AddCommGroup M] [inst_5 : Module R M] {p q : Submodule R M},
  Submodule.baseChange A p = Submodule.baseChange A q ↔ p = q

Defined in: Mathlib.RingTheory.Flat.FaithfullyFlat.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Ring Algebra Module.FaithfullyFlat AddCommGroup Module

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Algebrastatement and proof · cited by 11,388
Ringstatement and proof · cited by 7,463
Submodulestatement and proof · cited by 7,192
TensorProductstatement · cited by 2,545
Module.FaithfullyFlatstatement and proof · cited by 72
Submodule.baseChangestatement · cited by 36

Cited by1

Results whose statement or proof uses this declaration.

Submodule.baseChange_injectiveproof · cited by 0