R and S are rings.
Show that if is a homomorphism, and if a is a unit of S. Show, in fact, that for any unit of a of R.
Is this how I show this?
Instead, just notice that . The conclusion follows immediately.
f is a homomorphism if f satisfies the following properties:
If f satifies 1-3, then
So I didn't assume anything. I used what was given. It is stated that f is a homomorphism so it satisfies 1-3 which means 4 and 5 are also satisfied.