Factoring formal power series over principal ideal domains
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- by Jesse Elliott PDF
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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.References
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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
- 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: https://doi.org/10.1090/S0002-9947-2014-05903-5
- MathSciNet review: 3206450