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Math Help - Rings

  1. #1
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    Exclamation Rings

    Q1) Are these rings,
    a) 3Z X Z (direct product) and
    b) {ab(sqrt3)|a,bEQ}

    I think a) is a ring because 3Z and Z are rings and b) is not a ring as it is not a group because sqrt3 is irrational.

    Q2) Consider the matrix ring M2(Z2)
    a) Find the order of the ring
    b) List all the units of the ring

    Please show me what the matrix looks like as well because i think thats whats causing the problem.
    Thanks
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  2. #2
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    Quote Originally Posted by Ryan0710 View Post
    I think a) is a ring because 3Z and Z are rings and b) is not a ring as it is not a group because sqrt3 is irrational.
    You are correct to say (b) is not a ring. That is because it ab\sqrt{3} and cd\sqrt{3} are in it then (ab\sqrt{3})(cd\sqrt{3}) = 3abcd and this is not in it because \sqrt{3} is irrational, thus it is not closed (as long as a,b,c,d are non-zero).
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