16D10-DirectSummand.tex

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\begin{document}
Let $R$ be a ring and $B\subseteq A$ left (right) $R$-modules.  Then $B$ is called a \emph{direct summand} of $A$ if there exists a left (right) $R$-submodule $C$ such that $A=B\oplus C$.

For example, a projective module is a direct summand of a free module over any ring.
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