A mathematical object in which things can be added together Commutatively by multiplying Coefficients and in which most of the rules of manipulating Vectors hold. A module is abstractly very similar to a Vector Space, although modules have Coefficients in much more general algebraic objects and use Rings as the Coefficients instead of Fields.
The additive submodule of the Integers is a set of quantities closed under Addition and
Subtraction (although it is Sufficient to require closure under Subtraction). Numbers of the form
form a module since,
Foote, D. and Dummit, D. Abstract Algebra. Englewood Cliffs, NJ: Prentice-Hall, 1990.