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Math Help - maximal and prime ideals question

  1. #1
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    maximal and prime ideals question

    Let p be a fixed prime, and let R be the subring of Q consisting of all rational numbers a/b with (b,p) = 1.
    a) Show that R has a unique maximal ideal M.
    b) What are the prime ideals of R?
    c) Show that R/M is isomorphic to Z/pZ .
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  2. #2
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    Re: maximal and prime ideals question

    Hi,
    Attached is the complete solution:

    maximal and prime ideals question-mhfrings1.png
    Thanks from sandy123
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