Theorems · Definition · commutative algebra

Module.Relations.Solution.isPresentationCoreTensor

{A : Type u} →
  [inst : CommRing A] →
    {M₁ : Type v₁} →
      {M₂ : Type v₂} →
        [inst_1 : AddCommGroup M₁] →
          [inst_2 : AddCommGroup M₂] →
            [inst_3 : Module A M₁] →
              [inst_4 : Module A M₂] →
                {relations₁ : Module.Relations A} →
                  {relations₂ : Module.Relations A} →
                    {solution₁ : relations₁.Solution M₁} →
                      {solution₂ : relations₂.Solution M₂} →
                        solution₁.IsPresentation →
                          solution₂.IsPresentation → (solution₁.tensor solution₂).IsPresentationCore

The tensor product of two modules admits a presentation by generators and relations.

Defined in

Mathlib.Algebra.Module.Presentation.Tensor

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModule