Hypertranscendental elements of a formal power-series ring of positive characteristic
نویسندگان
چکیده
منابع مشابه
HYPERTRANSCENDENTAL 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...
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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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 کاملALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)
We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)
متن کاملALGEBRAIC INDEPENDENCE OF CERTAIN FORMAL POWER SERIES (I)
We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1992
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000003913