Factoring formal power series over principal ideal domains

Abstract

We provide an irreducibility test and factoring algorithm (with some qualificiations) for formal power series in the unique factorization domain R((X)), where R is any principal ideal domain. We also classify all integral domains arising as quotient rings of R((X)). Our main tool is a generalization of the p-adic Weierstrass preparation theorem to the context of complete filtered commutative rings.