Theorems · Theorem · ring theory

Module.map_jacobson_le

∀ {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}
  [inst_6 : RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂), Submodule.map f (Module.jacobson R M) ≤ Module.jacobson R₂ M₂

Defined in

Mathlib.RingTheory.Jacobson.Radical

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingRingAddCommGroupModuleAddCommGroupModuleRingHomSurjective