This is a Wedderburn Theorem proof in Frank W. Anderson, Kent R. Fuller: Rings and Categories of Modules
Please explain that: "Therefore $_RR$ has a composition series of length $n$". Exercise (11.5)
2026-04-02 21:46:07.1775166367
Problem with Wedderburn Theorem proof.
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(Maybe you didn't remember that $T^{(n)}$ is notation for $\oplus_{i=1}^{n}T$?)
Take the statement $_RR\cong T^{(n)}$ and look at that exercise. Since the sum is direct, the last line of (1) says that $c(_RR)=\sum_{i=1}^n c(_RT)$. But the composition length of $_RT$ is $1$, therefore $_RR$ has composition length $n$.