# Show the image of an ideal is an ideal of the image

## Homework Statement

Let ##\mu : R \to R'## be a ring homomorphism and let ##N## be an ideal of ##R##. Show that ##\mu [N]## is an ideal of ##\mu[R]##.

## The Attempt at a Solution

For something to be an ideal of a ring it must be an additive subgroup ##N## such that ##aN \subseteq N## and ##Nb \subseteq N## for all ##a,b \in R##.

Now, I know that ##\mu [N]## is a subgroup of ##R## under addition, but I don't necessarily know that it is a subgroup of ##\mu [R]##. How can I proceed if I can't establish this?

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