On a factorization result of \c{S}tef\u{a}nescu

TL;DR

This paper explores the factorization properties of polynomials over discrete valuation domains, generalizing a key result by Stefa
46escu through the introduction of the Newton index.

Contribution

It introduces a generalized factorization theorem for polynomials over discrete valuation domains using the Newton index concept.

Findings

Established new factorization properties over discrete valuation domains

Generalized Stefa
46escu's main result on polynomial factorization

Linked Newton index to polynomial factorization properties

Abstract

In this article, some factorization properties of polynomials over discrete valuation domains are elucidated. These properties along with the notion of Newton index of a polynomial leads to a generalization of the main result proved by \c{S}tef\u{a}nescu [`On the factorization of polynomials over discrete valuation domains', \emph{Versita} \textbf{22}:1 (2014), 273--280].