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

mona123

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Joined
Jan 20, 2015
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36
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
 
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Subhotosh Khan

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Staff member
Joined
Jun 18, 2007
Messages
18,134
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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