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Math Help - Abstract Algebra: Integral Domains!

  1. #1
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    Question Abstract Algebra: Integral Domains!

    Can someone please help!?

    In Z_7, give a reasonable interpretation for the expressions 1/2, -2/3, sqrt(-3), -1/6

    Need help as soon as possible and would greatly appreciate it, thank you all!!
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  2. #2
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    Sep 2008
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    1/2 means

    x times 2 = 1

    In Z_7 what can you multiply by 2 to equal 1? Or in other words what number less than 7 can you multiply by 2 and get a remainder of 1 when you mod 7?

    In Z_7
    0x2 = 0
    1x2 = 2
    2x2= 4
    3x2 = 6
    4x2 = 1
    5x2 = 3
    6x2 = 5

    So 1/2 would be 4 in Z_7

    You can go about the other problems in a similar manor.

    -2/3

    well what is -2? it is the OPPOSITE of 2, meaning -2 + 2 = 0. So what number in Z_7 is does x + 2 = 0? well thats 5, and then what number times 3 equals 5? From the chart above, thats 6!

    See if you can do the rest.
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