Factoring polynomials in the ring of formal power series over Z

Daniel Birmajer, Juan B. Gil, Michael Weiner

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider polynomials with integer coefficients and discuss their factorization properties in [[x]], the ring of formal power series over . We treat polynomials of arbitrary degree and give sufficient conditions for their reducibility as power series. Moreover, if a polynomial is reducible over [[x]], we provide an explicit factorization algorithm. For polynomials whose constant term is a prime power, our study leads to the discussion of p-adic integers.

Original languageEnglish (US)
Pages (from-to)1763-1776
Number of pages14
JournalInternational Journal of Number Theory
Volume8
Issue number7
DOIs
StatePublished - Nov 1 2012

Fingerprint

Formal Power Series
Factoring
Ring
Polynomial
Factorization
Constant term
Integer
Reducibility
P-adic
Power series
Sufficient Conditions
Arbitrary
Coefficient

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Factoring polynomials in the ring of formal power series over Z. / Birmajer, Daniel; Gil, Juan B.; Weiner, Michael.

In: International Journal of Number Theory, Vol. 8, No. 7, 01.11.2012, p. 1763-1776.

Research output: Contribution to journalArticle

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