Theorems · Theorem · commutative algebra

Submodule.le_of_map_mkQ_le_map_mkQ_of_le_jacobson_bot

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {I : Ideal R}
  {N N' : Submodule R M}, N.FG → I ≤ ⊥.jacobson → Submodule.map (I • N).mkQ N ≤ Submodule.map (I • N).mkQ N' → N ≤ N'

Defined in

Mathlib.RingTheory.Nakayama

Cited by

2 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule