# Injective polynomial ideals and the domination property

## TL;DR

This paper explores injective polynomial ideals, characterizing them through a domination property and applying this to classical operator ideals and composition polynomial ideals.

## Contribution

It introduces a new characterization of injective polynomial ideals via a domination property and demonstrates applications to classical and composition polynomial ideals.

## Key findings

- Characterization of injective polynomial ideals by a domination property
- Application of the characterization to classical operator ideals
- Application to composition polynomial ideals

## Abstract

After sketching the basic theory of injective ideals of homogeneous polynomials, we characterize injective polynomial ideals by means of a domination property and applications of this characterization to some classical operator ideals and to composition polynomial ideals are provided.