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

[mona123]

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

 

[Deleted member 4993]

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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