Formal power series

5kold

1. The problem statement, all variables and given/known data

Let F be a field. Consider the ring R=F[[t]] of the formal power series
in t. It is clear that R is a commutative ring with unity.

the things in R are things of the form infiniteSUM{ a_n } = a_0 + a_1 t + a_2 t +...

b is a unit iff the constant term a_0 =/= 0

Prove that R is a Euclidean domain with respect to the norm N(b)=n if a_n is the first term of b that is =/= 0.

In the polynomial ring R[x], prove that x^n-t is irreducible.



3. The attempt at a solution
I showed that it is a ED.

How do I show Irreducibility of this thing?
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution