Theorems · Theorem · commutative algebra

Submodule.le_of_le_smul_of_le_jacobson_bot

∀ {R : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {I : Ideal R}
  {N N' : Submodule R M}, N'.FG → I ≤ ⊥.jacobson → N' ≤ N ⊔ I • N' → N' ≤ N

Defined in

Mathlib.RingTheory.Nakayama

Cited by

9 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule