Vol. 2, Issue 8, Part F (2016)

Abstract
A vector space also called linear space is a collection of objects called vectors, which may be added together and multiplied by numbers, called scalars in this context. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. And a module is one of the fundamental algebraic structures used in abstract algebra. A module over a ring is a generalization of the notion of vector space over a field, wherein the corresponding scalars are the elements of an arbitrary given ring and a multiplication is defined between elements of the ring and elements of the module. Both seem to be same in terms of definition but when analysed deeply they are quite different as discussed in this paper.