FACTORING POLYNOMIALS IN THE RING OF FORMAL POWER SERIES OVER ℤ
نویسندگان
چکیده
منابع مشابه
Factorization of Quadratic Polynomials in the Ring of Formal Power Series over Z
We establish necessary and sufficient conditions for a quadratic polynomial to be irre-ducible in the ring Z[[x]] of formal power series over the integers. In particular, for polynomials of the form p n + p m βx + αx 2 with n, m ≥ 1 and p prime, we show that reducibility in Z[[x]] is equivalent to reducibility in Zp[x], the ring of polynomials over the p-adic integers.
متن کاملFactorization of Quadratic Polynomials in the Ring of Formal Power Series Over
We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the ring Z[[x]] of formal power series with integer coefficients. For n,m ≥ 1 and p prime, we show that p+pβx+αx is reducible in Z[[x]] if and only if it is reducible in Zp[x], the ring of polynomials over the p-adic integers.
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Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...
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The aim of this paper is to report on recent work on liftings of groups of au-tomorphisms of a formal power series ring over a eld k of characteristic p to characteristic 0, where they are realised as groups of automorphisms of a formal power series ring over a suitable valuation ring R dominating the Witt vectors W(k): We show that the lifting requirement for a group of automorphisms places se...
متن کاملhypertranscendental formal power series over fields of positive characteristic
let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2012
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042112501011