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Prove that this is an ideal of a commutative ring

  1. Oct 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Let R be a commutative ring, [itex]c \in R[/itex], M is ideal in R

    prove that [itex]J=\left\{rm+c\ |\ m \in M \ and\ r \in R \right\}[/itex] is ideal in R

    2. Relevant equations

    n/a

    3. The attempt at a solution

    for non-emptiness is easy

    so i want to show any x=rm+c, y=r'm'+c

    x-y=rm-r'm'-c+c is in J clue please T_T
     
  2. jcsd
  3. Oct 4, 2010 #2

    HallsofIvy

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    Science Advisor

    Re: subring

    x- y= r m- r' m'- c+ c= r m- r'm'. Now use the fact that m is in M which you are told is an ideal.
     
  4. Oct 4, 2010 #3
    Re: subring

    rm-r'm' is in M right? then T_T more clue
     
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