Theorems · Theorem · ring theory

Module.le_comap_jacobson

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_3} {M₂ : Type u_4} [inst : Ring R] [inst_1 : Ring R₂]
  [inst_2 : AddCommGroup M] [inst_3 : Module R M] [inst_4 : AddCommGroup M₂] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
  [RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂), Module.jacobson R M ≤ Submodule.comap f (Module.jacobson R₂ M₂)

Defined in

Mathlib.RingTheory.Jacobson.Radical

Cited by

6 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingRingAddCommGroupModuleAddCommGroupModuleRingHomSurjective