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 |
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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 |