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Irreducible polynomial, cyclic group

  1. Dec 9, 2008 #1
    Describe the field [tex]F=\frac{\mathbb{F}_3[x]}{(p(x))}[/tex] [[tex]p(x)[/tex] is an irreducible polynomial in [tex]\mathbb{F}_3[x][/tex]]. Find an element of [tex]F[/tex] that generates the cyclic group [tex]F^*[/tex] and show that your element works.

    [[tex]p(x)=x^2+1[/tex] is irreducible in [tex]\mathbb{F}_3[x][/tex] if that helps]
  2. jcsd
  3. Dec 9, 2008 #2


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    I've already given you a warning about posting your homework questions without showing your attempts to work on the problem. Continuing to do so will not be tolerated.
  4. Dec 9, 2008 #3
    Not to mention this should be in the Abstract Algebra forum.

    Write the elements of F explicitly (in terms of, say, t, where t2 + 1 = 0). Find one that has order 8.
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