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Math Help - Well-defined map

  1. #1
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    Well-defined map

    How can I show that the map, here Z= integers

    \phi: Z/3Z /times Z/3Z ---> Z/3Z defined by phi(x,y) = xy is well-defined.
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    Quote Originally Posted by peteryellow View Post
    How can I show that the map, here Z= integers

    \phi: Z/3Z /times Z/3Z ---> Z/3Z defined by phi(x,y) = xy is well-defined.
    If [x_1]=[x_2] and [y_1]=[y_2] then it means x_1\equiv x_2(\bmod 3) and y_1\equiv y_2(\bmod 3).
    Therefore, x_1y_1\equiv x_2y_2(\bmod 3) and so [x_1y_1] = [x_2y_2].
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