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Math Help - Solving Equations in a factor Ring Z[x] / <x>

  1. #1
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    Solving Equations in a factor Ring Z[x] / <x>

    How do I solve y -2y + 1 = 0 in the factor ring Z[x] / <x> ?
    I know how to solve this in Z or Z_n (where n is small), but I'm not too familiar with factor rings.
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  2. #2
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    Quote Originally Posted by Koaske View Post
    How do I solve y -2y + 1 = 0 in the factor ring Z[x] / <x> ?
    I know how to solve this in Z or Z_n (where n is small), but I'm not too familiar with factor rings.

    In any unitary ring, y^2-2y+1=(y-1)^2 , so...

    Tonio
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    I know that y = 1 is one solution, but are there others? Like in Z_n, there can be other solutions than just y = 1.
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    Quote Originally Posted by Koaske View Post
    I know that y = 1 is one solution, but are there others? Like in Z_n, there can be other solutions than just y = 1.
    You know that (y-1)^2=0. You now need to decide whether there are any nonzero elements in this ring whose square is 0. If not, then you can conclude that y-1=0.
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