(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Prove that this is an ideal of a commutative ring

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