# Thread: Simple module: Let R be a ring with 1 and F a family of simple left R modules.

1. ## Simple module: Let R be a ring with 1 and F a family of simple left R modules.

Please help me to prove the following result:

Let $R$ be a ring with $1$ and $\mathcal{F}$ a family of simple left $R$ modules.

Let $M=\oplus_{S\in \mathcal{F}} S$ and suppose that $T$ is a simple submodule of $M$.

Show that $T\cong S$ for some $S\in \mathcal{F}$.

Thanks

2. Originally Posted by mona123
Please help me to prove the following result:

Let $R$ be a ring with $1$ and $\mathcal{F}$ a family of simple left $R$ modules.

Let $M=\oplus_{S\in \mathcal{F}} S$ and suppose that $T$ is a simple submodule of $M$.

Show that $T\cong S$ for some $S\in \mathcal{F}$.

Thanks
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