
#1
Feb1610, 09:13 AM

P: 13

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^nt 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 


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