Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On $w$-Hilbert domains

Hyungtae Baek

Abstract

In this paper, we introduce the notion of a $w$-Hilbert domain and investigate its basic properties. More precisely, we explore its relationship with Hilbert domains, strong Mori domains, and UMT domains by providing various examples using $D+M$ constructions. Furthermore, we establish necessary and sufficient conditions for the polynomial ring and the Anderson ring to be $w$-Hilbert domains, and compare the $w$-dimension of the polynomial ring with that of its base ring.

On $w$-Hilbert domains

Abstract

In this paper, we introduce the notion of a -Hilbert domain and investigate its basic properties. More precisely, we explore its relationship with Hilbert domains, strong Mori domains, and UMT domains by providing various examples using constructions. Furthermore, we establish necessary and sufficient conditions for the polynomial ring and the Anderson ring to be -Hilbert domains, and compare the -dimension of the polynomial ring with that of its base ring.
Paper Structure (3 sections, 9 theorems)

This paper contains 3 sections, 9 theorems.

Table of Contents

  1. Introduction
  2. Basic properties and examples of w-Hilbert domains
  3. w-Hilbert domains arising from the polynomial ring and the Anderson ring

Key Result

Proposition 2.4

Let $D$ be a $w$-Hilbert domain. Then every $w$-G-ideal of $D$ is a maximal $w$-ideal of $D$.

Theorems & Definitions (26)

  • Example 2.1
  • Example 2.2
  • Example 2.3
  • Proposition 2.4
  • proof
  • Proposition 2.5
  • proof
  • Example 2.6
  • Proposition 2.7
  • proof
  • ...and 16 more