A special subring of the Nagata ring and the Serre's conjecture ring

TL;DR

This paper introduces a new subring called the Anderson ring, situated within Nagata and Serre's conjecture rings, and explores its properties and relationships to these rings.

Contribution

The paper defines the Anderson ring as a subring of Nagata and Serre's conjecture rings and analyzes its properties and comparisons.

Findings

The Anderson ring shares key properties with Nagata and Serre's rings.

The Anderson ring exhibits unique structural features.

Comparative analysis reveals similarities and differences among the rings.

Abstract

Many ring theorists researched various properties of Nagata rings and Serre's conjecture rings. In this paper, we introduce a subring (refer to the Anderson ring) of both the Nagata ring and the Serre's conjecture ring (up to isomorphism), and investigate properties of the Anderson ring. Additionally, we compare the properties of the Anderson ring with those of the Nagata ring and the Serre's conjecture ring.