Theorems · Theorem · commutative algebra

Submodule.LinearDisjoint.of_le_right_of_flat

∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] {M N : Submodule R S},
  M.LinearDisjoint N → ∀ {N' : Submodule R S}, N' ≤ N → ∀ [Module.Flat R ↥M], M.LinearDisjoint N'

If M and N are linearly disjoint, if M is flat, then for any submodule N' of N, M and N' are also linearly disjoint.

Defined in

Mathlib.LinearAlgebra.LinearDisjoint

Cited by

4 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingRingAlgebraModule.Flat