Module
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 .