Algebraic Generalized Power Series and Automata

Details Algebraic Generalized Power Series and Automata Algebraic Generalized Power Series and Automata

2001-10-08

arxiv.org/abs/math/0110089v1

Mathematics

Commutative Algebra

6 pages

Scientific paper

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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