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Math Help - Generator for an ideal

  1. #1
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    Generator for an ideal

    Let F be a field. In the polynomial ring F[x], let I be all the f(x) for which f(0) = f(1). Show that this I is an ideal in F[x], and find a generator for it -- that is, a polynomial h(x) such that our I consists of all multiple of h(x).


    I have absolutely no idea what to do here. How do you show that I is an ideal? What does that even mean? The things we have done in class for it haven't made any sense.
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  2. #2
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    Re: Generator for an ideal

    Try searching the internet. An ideal of a ring one of the most important notions in algebra. You will find plenty of material.
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