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How can I show the following?

Show that, if $a$ and $b$ are elements of a ring $R$ and $I$ is an ideal of $R$, then $$a+I=0+I \iff a \in I$$

I am so interested to know the proof.Thanks and good night all!

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    Note that this is really a statement about groups (the underlying additive abelian group of the ring, here): if $H < G$ then $aH = H$ if and only if $a \in H$.2012-02-01
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    @DylanMoreland Hence the title using the word "Translates" to convey the idea of cosets. =)2012-02-01

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