2011/07/25 by Jesse Elliott, Elliott, Jesse
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1107.4860
openalex publication_date 2011/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.