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Math Help - ideals

  1. #1
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    ideals

    I have one problem with ideals. Which properties of ideal will cause that the factor ring is comutative or ring with 1?
    Thanks
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  2. #2
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    Quote Originally Posted by sidi View Post

    I have one problem with ideals. Which properties of ideal will cause that the factor ring is comutative or ring with 1?
    Thanks
    first I has to be a two sided ideal because otherwise the factor ring R/I wouldn't be defined. now commutativity of R/I means that (x+I)(y+I)=(y+I)(x+I), for all x,y \in R, i.e.

    xy-yx \in I. so R/I is commutative iff I contains all additive commutators. for R/I to have 1, there must exist r \in R such that (r+I)(x+I)=(x+I)(r+I)=x+I, for all x \in R,

    or equivalently rx - x \in I and xr - x \in I. you can't put this condition in a more familiar form!
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  3. #3
    Newbie adit38's Avatar
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    great......, thx bro
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