Theorems · Definition · commutative algebra

DirectSum.tensorDecomposition

{ι : Type u_1} →
  {R : Type u_2} →
    {M : Type u_3} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            (ℳ : ι → Submodule R M) →
              [inst_3 : DecidableEq ι] →
                [DirectSum.Decomposition ℳ] →
                  (N : Type u_6) →
                    [inst_5 : AddCommGroup N] →
                      [inst_6 : Module R N] → DirectSum.Decomposition (DirectSum.decomposeTensor ℳ N)

The decomposition of a tensor product induced by a decomposition of the left module.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Decomposition

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleDecidableEqDirectSum.DecompositionAddCommGroupModule