n. a commutative group M endowed with an exterior multiplication (either on the left or right) that is associative and distributive and multiplies group elements by elements of a ring R (called scalars) to produce group elements; then M is a module over R, or an R-module. If, in addition, R is a unitary ring, then M is said to be a unitary R-module if the product of the identity of the ring with each element of the group is that element. Every commutative group may be viewed as a module over th e integers. A vector space is a module in which R is a field. Every ring R may be viewed as an R-module over itself, and an ideal in R is an R-module.