How Many Ring Homomorphisms Exist from Z to Z?

[FanofAFan]

Homework Statement

number of ring homomorphisms from $$Z$$ $$\rightarrow$$ $$Z$$?

Homework Equations

The Attempt at a Solution

According to this information on ring homo, There is no ring homomorphism Zn → Z for n > 1. But I guess that doesn't hold for when n = 1, any ideas

 

[HallsofIvy]

Any homomorphism must map identities to identities so a ring homomorphism must map 0 to 0 and 1 to 1. Now, any positive integer, n, can be written as a sum of "1"s. Therefore?

 

[FanofAFan]

Awesome, I figured it out, thanks