# Difference between revisions of "Module"

(Definition) |
m (stub) |
||

Line 17: | Line 17: | ||

If <math>R</math> is a [[field]] then <math>M</math> is a vector space over <math>R</math>. | If <math>R</math> is a [[field]] then <math>M</math> is a vector space over <math>R</math>. | ||

− | + | {{stub}} | |

[[Category:Abstract algebra]] | [[Category:Abstract algebra]] | ||

[[Category:Ring theory]] | [[Category:Ring theory]] | ||

[[Category:Module theory]] | [[Category:Module theory]] |

## Revision as of 19:25, 4 February 2009

A **module** is a type of object which appears frequently in abstract algebra. It is a generalization of the concept of a vector space.

Specifically, given a ring a **(left) -module** is an abelian group together with an operation (called scalar multiplication) written as or , which satisfies the following properties:

For all ,

(1)

(2)

(3)

(4)

We typically write to mean the module as well as the underlying abelian group.

If is a field then is a vector space over .

*This article is a stub. Help us out by expanding it.*