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Prove there are exactly 4 non-isomorphic algebras among algebras Af

  1. Feb 17, 2008 #1
    1. The problem statement, all variables and given/known data
    Let f = ax^3+bx^2+cx+d in R[x] be a cubic polynomial with real coefficients (a not equal to 0). Let g,h,k in Complex Numbers be roots of f. Let Af = R[x]/(f).

    Prove that there are exactly 4 non-isomorphic algebras among algebras Af.

    3. The attempt at a solution

    Proved f either has 1 real and 2 distinct complex nonreal roots or 3 real roots. In the former case some of roots can coincide (3 or 2 or none).

    From here I have become stumped, completely. Hope I have given enough for some help - please let me know if anything is unclear, but I have no idea where to go.

    Thanks in advance
     
  2. jcsd
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