Definition of Z^*_p: Introduction to Ring Theory

[OB1]

Homework Statement

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.

Homework Equations

Don't think there are any...

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.

 

[OB1]

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

 

[Hurkyl]

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.

 

[HallsofIvy]

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

No, it's not. Z_p 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 Z_p to be 0, 1, 2,..., p-1 and the members of Z^*_p to be 1, 2, ..., p-1 but the operations are different.