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Math Help - modern alg

  1. #1
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    modern alg

    Let R be acommutative ring and let b be a fixed element of R. Prove that the set b = {r is in R and r = cb for some element c in R} is an ideal of R.
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    Quote Originally Posted by wvlilgurl View Post
    Let R be acommutative ring and let b be a fixed element of R. Prove that the set b = {r is in R and r = cb for some element c in R} is an ideal of R.
    Define (b) = \{ rb | r\in R\}. To show (b) is an ideal of R you need to show if x,y\in (b) then x\pm y \in (b), and also that if r\in R then r(b),(b)r \subseteq (b). These should be clear by definition.
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