Theorems · Definition · ring theory

Module.Baer.extensionOfMax

{R : Type u} →
  [inst : Ring R] →
    {Q : Type v} →
      [inst_1 : AddCommGroup Q] →
        [inst_2 : Module R Q] →
          {M : Type u_1} →
            {N : Type u_2} →
              [inst_3 : AddCommGroup M] →
                [inst_4 : AddCommGroup N] →
                  [inst_5 : Module R M] →
                    [inst_6 : Module R N] →
                      (i : M →ₗ[R] N) → (f : M →ₗ[R] Q) → [Fact (Function.Injective ⇑i)] → Module.Baer.ExtensionOf i f

Since every nonempty chain has a maximal element, by Zorn's lemma, there is a maximal extension_of i f.

Defined in

Mathlib.Algebra.Module.Injective

Cited by

8 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddCommGroupAddCommGroupModuleModuleFact