Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
It's funny because on page 165, they say "We repeat that a module may be ..." but they never actually said it before. – Auburn Jul 9 at 18:12
up vote 1 down vote accepted

Consider $\mathbb Z_n$ as a $\mathbb Z$ module.

share|cite|improve this answer
Ok. Annihilator of $\mathbb Z_n$ contains n. Thus it has no independent subset, let alone a basis. Thank you. – user869081 Jan 11 '13 at 16:09

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.