Module
From AoPSWiki
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 .
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