Computing families of Cohen-Macaulay and Gorenstein rings

TL;DR

This paper characterizes Cohen-Macaulay and Gorenstein rings derived from convex body semigroups, providing algorithms to verify these properties in polygonal or circle semigroups and presenting specific families of such rings.

Contribution

It introduces new characterizations and algorithms for identifying Cohen-Macaulay and Gorenstein rings from convex body semigroups, including polygonal and circle cases.

Findings

Algorithms for checking Cohen-Macaulay/Gorenstein properties

Characterizations of rings from convex body semigroups

Families of Cohen-Macaulay and Gorenstein rings provided

Abstract

We characterize Cohen-Macaulay and Gorenstein rings obtained from certain types of convex body semigroups. Algorithmic methods to check if a polygonal or circle semigroup is Cohen-Macaulay/Gorenstein are given. We also provide some families of Cohen-Macaulay and Gorenstein rings.