Hello, I have two problems that relate, and I have been tossing them over for a couple of days but they seem to contradict each other.

The first: Show that 1-t is a unit inQ[[t]].

The second: Classify all units ofQ[[t]].

Now the second seems to be that all units are all non-zero zero degree polynomials, aka rationals. As if f(x) = a_{0}+ a_{1}x + ....+ a_{n}x^{n }was inQ[[t]] then its inverse would be (a_{0}+ a_{1}x + ....+ a_{n}x^{n })^{-1 }which is not a polynomial.

Thus f(x) does not have an inverse and is not a unit.

However, I also stumbled across a theorem/problem that states if a+bx is a unit if a and b are units in the ring. Thanks.