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Math Help - Integral Domain

  1. #1
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    Integral Domain

    Hello I am just trying to work out some problems from herstein. Can you please tell me if this one is right.


    If D is an integral domian and if na=0 for some a not 0 in D and for some integer n not 0 , prove that D is of finite characterstic.

    so we have for some a not 0, na = 0
    if b not 0 is another element in D then nab = 0b (ie) (na)b = 0

    na is an element of D, an integral domain which has zero divisors, so(na)b=0 where na = 0 is justified.

    However nab=0 => (nb)a=0
    Here nb is an element of D and a is nonzero,
    So nb = 0.

    Hence the proof.

    Am i right?
    Last edited by poorna; May 11th 2010 at 11:53 AM.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by poorna View Post
    Hello I am just trying to work out some problems from herstein. Can you please tell me if this one is right.


    If D is an integral domian and if na=0 for some a not 0 in D and for some integer n not 0 , prove that D is of finite characterstic.

    so we have for some a not 0, na = 0
    if b not 0 is another element in D then nab = 0b (ie) (na)b = 0

    na is an element of D, an integral domain which has zero divisors, so(na)b=0 where na = 0 is justified.

    However nab=0 => (nb)a=0
    Here nb is an element of D and a is nonzero,
    So nb = 0.

    Hence the proof.

    Am i right?
    That looks good to me.
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