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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Factoring formal power series over principal ideal domains


Author: Jesse Elliott
Journal: Trans. Amer. Math. Soc. 366 (2014), 3997-4019
MSC (2010): Primary 13F25, 13F10, 13F15, 13A05; Secondary 11S99
Published electronically: March 26, 2014
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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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Additional Information

Jesse Elliott
Affiliation: Department of Mathematics, California State University, Channel Islands, One University Drive, Camarillo, California 93012
Email: jesse.elliott@csuci.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05903-5
PII: S 0002-9947(2014)05903-5
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.