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Math Help - How do I find idempotent elements of binary operation?

  1. #1
    Member zzizi's Avatar
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    How do I find idempotent elements of binary operation?

    Hi, can anyone out there help with this?

    If Z x Z = {(a,b): a,b are integers} and if the binary operation on Z x Z by (a,b)*(c,d) = (ad,-bc),bd

    How do I show that the operation * has idempotent elements.

    I would really appreciate a step by step explanation.

    Many thanks in advance!
    Last edited by zzizi; April 21st 2012 at 10:38 AM. Reason: changed to subtraction
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  2. #2
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    Re: How do I find idempotent elements of binary operation?

    Do you require (a,b)*(a,b)=(a,b)?

    What is (a,b)*(a,b)?
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  3. #3
    Member zzizi's Avatar
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    Re: How do I find idempotent elements of binary operation?

    I was hoping someone could explain this to me. Btw I made a mistake it should have been a minus sign.
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  4. #4
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    Re: How do I find idempotent elements of binary operation?

    Do you mean (a,b)*(c,d) = (ad-bc,bd)?
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  5. #5
    Member zzizi's Avatar
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    Re: How do I find idempotent elements of binary operation?

    Yes
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  6. #6
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    Re: How do I find idempotent elements of binary operation?

    (a,b)*(a,b)=(ab-ab,b^2)=(0,b^2). If (a,b)*(a,b)=(a,b) then a=0 and b=b^2. So you have (0,1) or (0,0).
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  7. #7
    Member zzizi's Avatar
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    Re: How do I find idempotent elements of binary operation?

    Thank you so much

    If you or anyone else can point me to a tutorial site that can explain a bit more about finding idempotent elements of binary operations, it would be appreciated.

    Thanks
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