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Math Help - Annihilator

  1. #1
    pkr
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    Annihilator



    So far i've proved that Ann(a) is a subring (under addition and multiplication), now to prove it's an ideal i've shown;

    say a1, a2 elements of R, then a1 - a2 element of R, now i need to show rK, Kr to be an element of R...how do I go about this?
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  2. #2
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    Quote Originally Posted by pkr View Post


    So far i've proved that Ann(a) is a subring (under addition and multiplication), now to prove it's an ideal i've shown;

    say a1, a2 elements of R, then a1 - a2 element of R, now i need to show rK, Kr to be an element of R...how do I go about this?
    If x\in \text{Ann}(a) then ax=0. But then r(ax) = 0 \implies a(rx) = 0  \text{ and }a(xr) = 0. Thus, xr,rx \in \text{Ann}(a).
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  3. #3
    pkr
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    Ah, my version was alot more long winded, thanks very much, sorry I can't add to your reputation, it says i have to give it to others! Many thanks.
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