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arxiv: 1107.4860 · v4 · pith:TVPGV47Cnew · submitted 2011-07-25 · 🧮 math.AC · math.NT

Factoring formal power series over principal ideal domains

classification 🧮 math.AC math.NT
keywords domaindomainsfactoringformalidealpowerprincipalrings
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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.

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