The reduced divisor class group and the torsion number

TL;DR

This paper introduces the reduced divisor class group and torsion number for normal Cohen--Macaulay graded domains, analyzing their properties with a focus on normal affine semigroup rings.

Contribution

It defines and studies the reduced divisor class group and torsion number, providing new insights into their structure for normal affine semigroup rings.

Findings

Characterization of the reduced divisor class group.

Analysis of torsion number properties.

Applications to normal affine semigroup rings.

Abstract

The reduced divisor class group of a normal Cohen--Macaulay graded domain together with its torsion number is introduced. They are studied in detail especially for normal affine semigroup rings.