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Algebra question

  1. Dec 8, 2008 #1


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    1. The problem statement, all variables and given/known data
    I'm studying introductory ring theory and have encountered the notation [tex] Z^{*}_{p} [/tex] 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. jcsd
  3. Dec 8, 2008 #2


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    Never mind, I got it, it's [tex] Z_{p}-0 [/tex].
  4. Dec 8, 2008 #3


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    Staff Emeritus
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    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.
  5. Dec 9, 2008 #4


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    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.
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