Hi, I have almost no experience with abstract algebra (just a bit with matrices), and to start I checked out the bookNumbers and Symmetryby Bernard L. Johnston. The first section introduces the Gaussian integers $\displaystyle Z[i]$, which he contrasts with the regular integers $\displaystyle Z$. In the second chapter he introduces "circular" numbers $\displaystyle Z_n$, which he explains as being the number line wrapped around a circle, basically. I'm familiar with basic modular arithmetic so I got that bit, but then he starts talking about zero divisors and units ("a number in a number system is aunitif every number in the system is a multiple of it"). The section is pretty brief and I didn't quite get a grip on it, but I can't find anything about it on the Internet. When I search for "circular numbers" I get a different definition involving squares. Is there another word for this type of thing?

For example, one of the questions is:

What are the units in $\displaystyle Z_6$?

I couldn't find any units, but I am not sure if that is right. Could someone perhaps point me in a direction where I could read alternate explanations? That usually helps me greatly.

Thanks!