Theorems · Definition · linear algebra

Submodule.prod

{R : Type u_1} →
  {M : Type u_4} →
    [inst : Semiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          Submodule R M →
            {M' : Type u_8} →
              [inst_3 : AddCommMonoid M'] → [inst_4 : Module R M'] → Submodule R M' → Submodule R (M × M')

The product of two submodules is a submodule.

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

55 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModule