# Prove that this is an ideal of a commutative ring

1. Oct 4, 2010

### annoymage

1. The problem statement, all variables and given/known data

Let R be a commutative ring, $c \in R$, M is ideal in R

prove that $J=\left\{rm+c\ |\ m \in M \ and\ r \in R \right\}$ 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. Oct 4, 2010

### HallsofIvy

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.

3. Oct 4, 2010

### annoymage

Re: subring

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