Factoring formal power series over principal ideal domains

Elliott, Jesse

doi:10.1090/S0002-9947-2014-05903-5

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
DOI: https://doi.org/10.1090/S0002-9947-2014-05903-5
Published electronically: March 26, 2014
MathSciNet review: 3206450
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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 , where is any principal ideal domain. We also classify all integral domains arising as quotient rings of . Our main tool is a generalization of the -adic Weierstrass preparation theorem to the context of complete filtered commutative rings.

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