free module
Let R be a ring.
A free module
over R
is a direct sum
of copies of R.
Similarly, as an abelian group
is simply a module over ℤ,
a free abelian group
is a direct sum of copies of ℤ.
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 R
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 |