# direct summand

Let $R$ be a ring and $B\subseteq A$ left (right) $R$-modules. Then $B$ is called a 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.

Title direct summand DirectSummand 2013-03-22 14:51:42 2013-03-22 14:51:42 CWoo (3771) CWoo (3771) 6 CWoo (3771) Definition msc 16D10 DirectSum