Please help me to prove the following result:

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

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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