Homogeneous prime elements in normal two-dimensional graded rings

TL;DR

This paper characterizes when homogeneous prime elements exist in normal two-dimensional graded rings using divisor theory on projective curves, providing a complete criterion.

Contribution

It offers necessary and sufficient conditions for the existence of homogeneous prime elements in these rings based on divisor theory.

Findings

Criteria for existence of homogeneous prime elements

Connection between ring properties and divisor theory

Complete characterization in terms of Weil divisors

Abstract

We prove necessary and sufficient conditions for the existence of homogeneous prime elements in normal N-graded rings of dimension two, in terms of rational coefficient Weil divisors on projective curves.