# Algebra question

1. Dec 8, 2008

### OB1

1. The problem statement, all variables and given/known data
I'm studying introductory ring theory and have encountered the notation $$Z^{*}_{p}$$ with no definition attached. If anyone could provide the definition for this, that would be great.

2. Relevant equations
Don't think there are any...

3. The attempt at a solution
The only way I've ever encountered * above anything was in the dual space, and I'm pretty convinced it has nothing to do with it.

2. Dec 8, 2008

### OB1

Never mind, I got it, it's $$Z_{p}-0$$.

3. Dec 8, 2008

### Hurkyl

Staff Emeritus
For a ring R, the notation R* is usually used to denote the set of elements that have a multiplicative inverse. (This set is actually a group, with the operation being multiplication)

The equation R* = R - {0} is valid if and only if R is a field.

4. Dec 9, 2008

### HallsofIvy

Staff Emeritus
No, it's not. Zp specifically means the integers with addition modulo p.

Z*p is the integers, other than 0, with multiplication modulo p.
You can take the members of Zp to be 0, 1, 2,..., p-1 and the members of Z*p to be 1, 2, ..., p-1 but the operations are different.