I am working my way through Linear Algebra - Hoffman and Kunze. There is a very brief introduction to Modules in the chapter on Determinants. The authors state "..a module may be finitely generated without having a finite basis.". I am looking for an example for such a module.
I am not familiar with Group/Ring theory (although a know the basic definitions), so the examples else where are taking too long to understand.
For ex. A module without a basis forces me to go get an understanding of subgroupgs, cyclic groups, factor groups.