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

#### mona123

##### New member

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

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

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

Thanks

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#### Subhotosh Khan

##### Super Moderator
Staff member

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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