Factoring formal power series over principal ideal domains [article]

Jesse Elliott
2012 arXiv   pre-print
We provide an irreducibility test and factoring algorithm (with some qualifications) 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.
arXiv:1107.4860v4 fatcat:rm4pclcskjfkhj6yuctplroxzy