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Math Help - Units

  1. #1
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    Units

    What are the units of Z? In other words find Z^x.

    Here is some background:

    Every element in a ring has an additive inverse, but only some elements
    have multiplicative inverses. Any element with a multiplicative inverse is
    called a
    unit. Recall that we assume all rings have a multiplicative identity.

    Let R be a ring with multiplicative identity 1. If a, b eR are
    such that
    ab = ba = 1 then we say that a and b are multiplicative inverses.

    An element
    a e R is called a unit if it has an inverse. The set of units is
    written
    R:

    R^x = {u e R | u is a unit}
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  2. #2
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    1

    Units

    Hello jzellt
    Quote Originally Posted by jzellt View Post
    What are the units of Z? In other words find Z^x.

    Here is some background:

    Every element in a ring has an additive inverse, but only some elements
    have multiplicative inverses. Any element with a multiplicative inverse is
    called a
    unit. Recall that we assume all rings have a multiplicative identity.

    Let R be a ring with multiplicative identity 1. If a, b eR are
    such that
    ab = ba = 1 then we say that a and b are multiplicative inverses.

    An element
    a e R is called a unit if it has an inverse. The set of units is
    written
    R:

    R^x = {u e R | u is a unit}
    In \mathbb{R}, all non-zero elements, x, have a multiplicative inverse, \frac{1}{x}. But in \mathbb{Z}, \frac{1}{n} will not be an integer unless n = ... ?

    Grandad
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