On the convergence of generalized power series satisfying an algebraic ODE
نویسندگان
چکیده
منابع مشابه
Algebraic Generalized Power Series and Automata
A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol’s result, we prove that the same assertion holds for generalized power series (whose index sets may be arbitrary well-ordered sets of nonnegative rationals).
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Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.
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ژورنال
عنوان ژورنال: Asymptotic Analysis
سال: 2015
ISSN: 1875-8576,0921-7134
DOI: 10.3233/asy-151297