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

For an arbitrary ring $R$ and a positive integer $n >1$, are the category of $R$-modules and the category of $M_n(R)$-modules isomorphic?

Here, $M_n(R)$ denotes the $n$ plus $n$ matrices over the ring $R$.

I know these two categories are equivalent, and I guess they are not necessarily isomorphic, but I don't know how to prove it...

Many thanks :)

share|cite|improve this question
Why would you want to know? Just curiosity? Isomorphism of categories is usually too strong a property; that's why equivalence of categories is more prevalent, as it is normally just as useful but easier to handle. – Arturo Magidin Mar 15 '11 at 21:55
Thank you for taking time to comment. I want to know about this not just for curiosity. This a problem in Basic Algebra written by Nanthan Jacobson. – ShinyaSakai May 1 '11 at 17:40
Then say so in your question. It's called "giving context". – Arturo Magidin May 1 '11 at 18:13

Your Answer


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

Browse other questions tagged or ask your own question.