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
for
form a module since,

Given two Integers and , the smallest module containing and is .

**References**

Foote, D. and Dummit, D. *Abstract Algebra.* Englewood Cliffs, NJ: Prentice-Hall, 1990.

© 1996-9

1999-05-26