# 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 $\mathbb{Z}$,
a free abelian group
is a direct sum of copies of $\mathbb{Z}$.

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 |