free module
Let be a ring.
A free module over
is a direct sum
of copies of .
Similarly, as an abelian group
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 combination over
of elements of the free basis.
Every free module is also a projective module,
as well as a flat module
.
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 |