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-   -   Show the following is a field. (You must show that operations are binary first.) (https://www.askmehelpdesk.com/showthread.php?t=533002)

  • Dec 9, 2010, 12:07 AM
    mrenney
    Show the following is a field. (You must show that operations are binary first.)
    Show that {Q( square root of 13,+,*} is a field?
    Let Q( square root of 13 ={x+y square root of 13 where x,y are elements of Q}

    Q of course is rational numbers
    Addition and multiplication are defined as follows
    (a+b square root of 13)+(c+d square root of 13) =(a+c)+(b+d) square root of 13
    (a+b square root of 13)(c+d square root of 13) = (ac+13bd)+(ad+bc) square root of 13

    Show that {Q( square root of 13,+,*} is a field

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