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arXiv · 1107.4860

Factoring formal power series over principal ideal domains

Jesse Elliott
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Abstract

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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Jesse Elliott. 2011-07-25. Factoring formal power series over principal ideal domains. https://arxiv.org/abs/1107.4860

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