On some properties of polynomial composites

TL;DR

This paper investigates various algebraic properties of polynomial composites, completing their classification with respect to several domain properties and exploring their structure as Dedekind rings.

Contribution

It provides a comprehensive analysis of polynomial composites, establishing their properties as ACCP, atomic, BFD, HFD, idf, FFD domains, and examines their structure as Dedekind rings.

Findings

Polynomial composites can possess ACCP, atomic, BFD, HFD, idf, FFD properties.

The paper characterizes polynomial composites as Dedekind rings.

It fills gaps in the algebraic understanding of polynomial composites.

Abstract

Polynomial composites were introduced by Anderson, Anderson, and Zafrullah. Over time, composites have appeared in many different papers, but they have not been sorted out in the algebra world. This paper is another part of the study of composites as an algebraic structure. In this paper we complete possible properties for polynomial composites as ACCP, atomic, BFD, HFD, idf, FFD domains. In a separate section, we consider polynomial composites as Dedekind rings.