The Abhyankar-Moh theorem for plane valuations at infinity

TL;DR

This paper introduces a new class of plane valuations at infinity and proves an analogue of the Abhyankar-Moh theorem for these valuations, extending classical results to a broader context.

Contribution

It defines plane valuations at infinity and establishes a new theorem analogous to Abhyankar-Moh for this class, advancing valuation theory.

Findings

Established the class of plane valuations at infinity.

Proved an Abhyankar-Moh type theorem for these valuations.

Extended classical valuation results to a new setting.

Abstract

We introduce the class of plane valuations at infinity and prove an analogue to the Abhyankar-Moh (semigroup) Theorem for it.