On Landweber`s unique factorization problem

Abstract

We solve a long-standing open problem, posed by Landweber in 1974: Let $R=K[x_1,x_2,...]$ be the ring of polynomials in countably many variables over a field $K$. Is the formal power series ring $R[[t]]$ a unique factorization domain? We prove that it is. The proof is based on a new general result in commutative algebra: If $R$ is a Krull domain, and $f\in R[[t]]$ is irreducible, then $f$ is irreducible modulo a finite power of $t$.

24 pages