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 in Q[[t]].
The second: Classify all units of Q[[t]].
Now the second seems to be that all units are all non-zero zero degree polynomials, aka rationals. As if f(x) = a0 + a1x + ....+ anxn was in Q[[t]] then its inverse would be (a0 + a1x + ....+ anxn )-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.