free module

Let R be a ring. A free moduleMathworldPlanetmathPlanetmath over R is a direct sumPlanetmathPlanetmathPlanetmathPlanetmath of copies of R.

Similarly, as an abelian groupMathworldPlanetmath is simply a module over , a free abelian group is a direct sum of copies of .

This is equivalent to saying that the module has a free basis, i.e. a set of elements with the property that every element of the module can be uniquely expressed as an linear combinationMathworldPlanetmath over R of elements of the free basis.

Every free module is also a projective moduleMathworldPlanetmath, as well as a flat moduleMathworldPlanetmath.

Title free module
Canonical name FreeModule1
Date of creation 2013-03-22 14:03:50
Last modified on 2013-03-22 14:03:50
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 5
Author Mathprof (13753)
Entry type Definition
Classification msc 16D40