# Algebraic elements over the ring of power series

## TL;DR

This paper establishes a precise criterion for when certain generalized power series are algebraic over power series rings with finite field coefficients, extending a classical theorem by Huang-Stefanescu.

## Contribution

It provides a necessary and sufficient condition for algebraicity of generalized power series over finite fields, broadening the scope of existing algebraic criteria.

## Key findings

- Derived a new algebraic criterion for generalized power series
- Extended Huang-Stefanescu's classical theorem
- Enhanced understanding of algebraic power series over finite fields

## Abstract

We give a necessary and sufficient condition for a type of generalized power series to be algebraic over the ring of power series with coefficients in a finite field. This result extend a classical theorem of Huang-Stefanescu.