Explore BrainMass

Explore BrainMass

    Irreducible Polynomials and Isomorphic Fields

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Let F=Z7 and let p(x)=x^3 - 2 and q(x)= x^3 + 2 in F[x]. Show that p(x) and q(x) are irreducible in F[x] and that the fields F[x]/p(x) and F[x]/q(x) are isomorphic.

    See the attached file.

    © BrainMass Inc. brainmass.com March 4, 2021, 7:45 pm ad1c9bdddf
    https://brainmass.com/math/number-theory/irreducible-polynomials-isomorphic-fields-120987

    Attachments

    Solution Summary

    Irreducible polynomials and isomorphic fields are investigated and discussed in the solution.

    $2.49

    ADVERTISEMENT