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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Factoring formal power series over principal ideal domains
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by Jesse Elliott PDF
Trans. Amer. Math. Soc. 366 (2014), 3997-4019 Request permission


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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Additional Information
  • Jesse Elliott
  • Affiliation: Department of Mathematics, California State University, Channel Islands, One University Drive, Camarillo, California 93012
  • Email:
  • Received by editor(s): December 17, 2011
  • Received by editor(s) in revised form: June 22, 2012, and June 26, 2012
  • Published electronically: March 26, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3997-4019
  • MSC (2010): Primary 13F25, 13F10, 13F15, 13A05; Secondary 11S99
  • DOI:
  • MathSciNet review: 3206450