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
Canonical name	DirectSummand
Date of creation	2013-03-22 14:51:42
Last modified on	2013-03-22 14:51:42
Owner	CWoo (3771)
Last modified by	CWoo (3771)
Numerical id	6
Author	CWoo (3771)
Entry type	Definition
Classification	msc 16D10
Related topic	DirectSum