The problem is from Artin.
Prove that the ring $\mathbb{R}[[t]]$ of formal power series given by $p(t)=a_0 + a_1 t+ a_2 t^2 + \cdots$ is an UFD.
I have no idea how to do this. From the couple of things that I know about UFDs is that I could show that every irreducible element is prime, or I could show that every chain of ideals terminates. Any help will be appreciated.
Best Answer
Show that each ideal $\neq 0$ has the form $\mathfrak a = t^k\mathbb R[[t]] $.