direct summand

Let R be a ring and BA left (right) R-modules. Then B is called a direct summandMathworldPlanetmath of A if there exists a left (right) R-submoduleMathworldPlanetmath C such that A=BC.

For example, a projective moduleMathworldPlanetmath is a direct summand of a free moduleMathworldPlanetmathPlanetmath 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