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Homework Help: Notation related to quotient fields

  1. Feb 3, 2013 #1
    1. The problem statement, all variables and given/known data

    Let f(x) = x6 + x3 + 1 in Z_2[x]. Show that f(x) is irreducible. Let E = Z_2[x]/(f(x)),
    and let α denote the image of x in the quotient field. Show that E* = <α>.

    2. Relevant equations

    I have solved the first part, but what does E* mean? I have seen the asterix in connection with dual spaces before, but I reckon it means something else here.

    3. The attempt at a solution
  2. jcsd
  3. Feb 4, 2013 #2
    It would be nice if someone could give some directions...
  4. Feb 4, 2013 #3

    I like Serena

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    Homework Helper

    Hi fortissimo! :smile:

    I do not understand what you mean with the image of x in the quotient field.

    But I do know that the star notation in algebra usually means the set without the zero-dividers.
    Hope this helps.
  5. Feb 4, 2013 #4
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