- #1

- 64

- 0

[itex]\tau[/itex] : [itex]Z[/itex][itex]\overline{+}[/itex] -> [itex]Z[/itex][itex]\overline{+}[/itex]

From this it should be possible to determine which is injective, surjective, and which are isomorphic.

Homomorphisms between Z plus to Z plus will all be of the form [itex]\tau[/itex](x) = nx

since [itex]\tau[/itex](x) = [itex]\tau[/itex](1)[itex]\underline{1}[/itex] + [itex]\tau[/itex](1)[itex]\underline{2}[/itex] + ... + [itex]\tau[/itex](1)[itex]\underline{x}[/itex]

since we have a homomorphism and x is one summed x times.

all are injective

now im not sure how to tell which are surjective