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## Homework Statement

[itex]\mathbb{Z}[x]/(x^3-x) \rightarrow \mathbb{Z} [/itex]

Show that is ring homomorphism, and count the number of homomorphism..?

## Homework Equations

## The Attempt at a Solution

the map [itex]f[/itex] is homomorphism if,

[itex]f(x+y)=f(x)+f(y)[/itex]

[itex]f(xy)=f(x)f(y)[/itex]

I think, I must find a map for the question , but how should I choose the map, I don't know....