Theorems · Theorem · ring theory

LinearMap.isSimpleModule_iff_of_bijective

∀ {R : Type u_2} {S : Type u_3} [inst : Ring R] [inst_1 : Ring S] {M : Type u_4} [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] {N : Type u_5} [inst_4 : AddCommGroup N] [inst_5 : Module S N] {σ : R →+* S}
  [RingHomSurjective σ] (l : M →ₛₗ[σ] N), Function.Bijective ⇑l → (IsSimpleModule R M ↔ IsSimpleModule S N)

Defined in

Mathlib.RingTheory.SimpleModule.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

RingRingAddCommGroupModuleAddCommGroupModuleRingHomSurjective