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 language | English (US) |
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Pages (from-to) | 1763-1776 |
Number of pages | 14 |
Journal | International Journal of Number Theory |
Volume | 8 |
Issue number | 7 |
DOIs | |
State | Published - Nov 2012 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory