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Math Help - Rings

  1. #1
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    Rings

    let R be a commutatuve ring that does not have unity. For a fixed a in R, prove that the set (a)={na+ra|n in Z, r in R} is an ideal of R that contains the element a.
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    Quote Originally Posted by bookie88 View Post
    let R be a commutatuve ring that does not have unity. For a fixed a in R, prove that the set (a)={na+ra|n in Z, r in R} is an ideal of R that contains the element a.
    This is pretty plug and chug. What have you tried?
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  3. #3
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    Quote Originally Posted by bookie88 View Post
    let R be a commutatuve ring that does not have unity. For a fixed a in R, prove that the set (a)={na+ra|n in Z, r in R} is an ideal of R that contains the element a.
    In case you are interested in some additional details,

    If a is in the center of R (assuming R is not necessary commutative), then your (a)={na+ra|n in Z, r in R} is an ideal of R containing a and contained in every ideal containing a. (Hungerford "Algebra", p 124)
    Last edited by aliceinwonderland; February 22nd 2010 at 11:58 PM.
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