On free resolutions of some semigroup rings

TL;DR

This paper explicitly computes minimal free resolutions for certain small embedding dimension semigroup rings, enabling the determination of invariants and relations, and identifying semigroups with strongly indispensable resolutions.

Contribution

It extends known results by providing explicit graded minimal free resolutions for semigroup rings of small embedding dimension, and analyzes their invariants and properties.

Findings

Explicit resolutions for embedding dimension 3 and 4 semigroup rings.

Identification of semigroups with strongly indispensable resolutions.

Relations among invariants of these semigroups.

Abstract

For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results by giving the whole graded minimal free resolutions explicitly. Then we use these resolutions to determine some invariants of the semigroups and certain interesting relations among them. Finally, we determine semigroups of small embedding dimensions which have strongly indispensable resolutions.