K + M constructions with general overrings and relationships with polynomial composites

TL;DR

This paper explores the construction of K + M rings, where K is a domain and M is a maximal ideal from polynomial rings over a field, analyzing their properties and relationships with polynomial composites.

Contribution

It provides new insights into the structure of K + M constructions, especially in the context of polynomial composites and various domain types.

Findings

Characterization of K + M constructions in different domain contexts

Connections established between K + M rings and polynomial composites

New construction results for Noetherian, Prufer, and GCD-domains

Abstract

In this paper we consider the construction of K + M, where K is the domain, M is the maximal ideal of a some ring of polynomials with coefficients from the field L, where K is its subring. In addition to the usual domains, we also consider the Noetherian, Prufer and GCD-domains. In particular, polynomial composites are a case of K + M construction. In this paper we will find numerous construction conclusions related to polynomial composites.