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Thread: Units in a polynomial ring

  1. September 1st 2010, 07:07 PM #1
    Jose27
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    Units in a polynomial ring

    Challenge question:

    Let R be a commutative ring and f(x)=a_0+...+a_nx^n \in R[x] then f is a unit if and only if a_0 is a unit and a_1,...a_n are nilpotent.

    I have a solution using more involved ring theory, but I'm really interested to see more elementary solutions (or even more involved or indirect, why not).

    Moderator approved CB
    Last edited by CaptainBlack; September 1st 2010 at 08:48 PM.
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  2. September 2nd 2010, 05:52 AM #2
    NonCommAlg
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    see my post in here.
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