# Sum of Submodules is Submodule

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## Theorem

Let $R$ be a ring.

Let $M = \struct {G, +, \circ}_R$ be an $R$-module.

Let $H$ and $K$ be submodules of $M$.

Then $H + K$ is also a submodule of $M$.

This article, or a section of it, needs explaining.In particular: Link to what $H + K$ means -- seems like it may not exist yet, which is a bit weirdYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Explain}}` from the code. |

## Proof

This theorem requires a proof.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 27$. Subspaces and Bases: Theorem $27.2$